Let T be a bounded operator on Lp(ℝn). Under the assumption that the kernel of T satisfies some Hörmander-type estimates, we obtain a boundedness criterion for the multilinear commutators Tb→ on the weighted Lebesgue spaces Lp(ω) with b→∈BMO(ℝn) and ω belonging to the Muckenhoupt weight class Ap∕m′. Further, for b→∈CMO(ℝn), the vanishing mean oscillation space, a criterion of Lp-weighted compactness of Tb→ is established. As applications, the weighted Lp-boundedness and Lp-compactness criteria can be applied to the 𝜃-type Calderón–Zygmund operator and its commutators.
{"title":"A WEIGHTED COMPACTNESS CRITERION FOR COMMUTATORS ASSOCIATED WITH GENERALIZED CALDERÓN–ZYGMUND OPERATORS","authors":"Li Yang, Qianjun He, Pengtao Li, Kai Zhao","doi":"10.1216/jie.2023.35.235","DOIUrl":"https://doi.org/10.1216/jie.2023.35.235","url":null,"abstract":"Let T be a bounded operator on Lp(ℝn). Under the assumption that the kernel of T satisfies some Hörmander-type estimates, we obtain a boundedness criterion for the multilinear commutators Tb→ on the weighted Lebesgue spaces Lp(ω) with b→∈BMO(ℝn) and ω belonging to the Muckenhoupt weight class Ap∕m′. Further, for b→∈CMO(ℝn), the vanishing mean oscillation space, a criterion of Lp-weighted compactness of Tb→ is established. As applications, the weighted Lp-boundedness and Lp-compactness criteria can be applied to the 𝜃-type Calderón–Zygmund operator and its commutators.","PeriodicalId":50176,"journal":{"name":"Journal of Integral Equations and Applications","volume":"2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135195662","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"EXISTENCE OF SOLUTIONS OF NONLINEAR FREDHOLM-TYPE INTEGRAL EQUATIONS IN HÖLDER SPACE","authors":"Manalisha Bhujel, B. Hazarika","doi":"10.1216/jie.2023.35.1","DOIUrl":"https://doi.org/10.1216/jie.2023.35.1","url":null,"abstract":"","PeriodicalId":50176,"journal":{"name":"Journal of Integral Equations and Applications","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43613399","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"EXISTENCE AND APPROXIMATE SOLUTIONS FOR HADAMARD FRACTIONAL INTEGRAL EQUATIONS IN A BANACH SPACE","authors":"M. Kazemi, H. Chaudhary, Amar Deep","doi":"10.1216/jie.2023.35.27","DOIUrl":"https://doi.org/10.1216/jie.2023.35.27","url":null,"abstract":"","PeriodicalId":50176,"journal":{"name":"Journal of Integral Equations and Applications","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42970986","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"EXISTENCE, UNIQUENESS AND REGULARITY OF THE SOLUTION FOR A SYSTEM OF WEAKLY SINGULAR VOLTERRA INTEGRAL EQUATIONS OF THE FIRST KIND","authors":"S. Shahmorad, Mahdi Mostafazadeh","doi":"10.1216/jie.2023.35.105","DOIUrl":"https://doi.org/10.1216/jie.2023.35.105","url":null,"abstract":"","PeriodicalId":50176,"journal":{"name":"Journal of Integral Equations and Applications","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48603335","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Functional reproducing kernel Hilbert spaces (FRKHSs) are appropriate function spaces in which we seek a target function from a finite number of non-point-evaluation functional data. We consider reconstructing a function from a finite number of generalized moment data via regularization in an FRKHS with respect to the generalized moment functionals. We construct specific FRKHSs and their associated FRKHS kernels with respect to two classes of generalized moment functionals, the Hamburger moment functionals and the trigonometric moment functionals. We solve the regularization problem in the resulting FRKHSs by the representer theorem. Numerical examples are presented to illustrate the better performance of regularization in an FRKHS than regularization in the square integrable functions space.
{"title":"REGULARIZATION METHOD FOR THE GENERALIZED MOMENT PROBLEM IN A FUNCTIONAL REPRODUCING KERNEL HILBERT SPACE","authors":"Qianru Liu, Lei Huang, Rui Wang","doi":"10.1216/jie.2023.35.61","DOIUrl":"https://doi.org/10.1216/jie.2023.35.61","url":null,"abstract":"Functional reproducing kernel Hilbert spaces (FRKHSs) are appropriate function spaces in which we seek a target function from a finite number of non-point-evaluation functional data. We consider reconstructing a function from a finite number of generalized moment data via regularization in an FRKHS with respect to the generalized moment functionals. We construct specific FRKHSs and their associated FRKHS kernels with respect to two classes of generalized moment functionals, the Hamburger moment functionals and the trigonometric moment functionals. We solve the regularization problem in the resulting FRKHSs by the representer theorem. Numerical examples are presented to illustrate the better performance of regularization in an FRKHS than regularization in the square integrable functions space.","PeriodicalId":50176,"journal":{"name":"Journal of Integral Equations and Applications","volume":"185 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135423789","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"CONTINUOUS PIECEWISE POLYNOMIAL COLLOCATION METHODS FOR GENERALIZED AUTO-CONVOLUTION VOLTERRA INTEGRAL EQUATIONS","authors":"Yuping Li, Hui Liang","doi":"10.1216/jie.2023.35.41","DOIUrl":"https://doi.org/10.1216/jie.2023.35.41","url":null,"abstract":"","PeriodicalId":50176,"journal":{"name":"Journal of Integral Equations and Applications","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43140682","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Yucheng Song, Tingting Fang, Jiu Ding, Congming Jin
{"title":"SOLVING LINEAR VOLTERRA INTEGRAL EQUATIONS WITH A PIECEWISE LINEAR MAXIMUM ENTROPY METHOD","authors":"Yucheng Song, Tingting Fang, Jiu Ding, Congming Jin","doi":"10.1216/jie.2023.35.119","DOIUrl":"https://doi.org/10.1216/jie.2023.35.119","url":null,"abstract":"","PeriodicalId":50176,"journal":{"name":"Journal of Integral Equations and Applications","volume":"8 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41305633","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"NONEXISTENCE OF GLOBAL SOLUTIONS FOR TIME FRACTIONAL WAVE EQUATIONS IN AN EXTERIOR DOMAIN","authors":"J. He","doi":"10.1216/jie.2023.35.11","DOIUrl":"https://doi.org/10.1216/jie.2023.35.11","url":null,"abstract":"","PeriodicalId":50176,"journal":{"name":"Journal of Integral Equations and Applications","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46153947","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A BSTRACT . This paper is concerned with the numerical treatment of second kind Volterra integral equations whose integrands present diagonal and/or endpoint algebraic singularities. A projection method based on an optimal interpolating operator is developed in the spaces of weighted continuous functions endowed with the supremum norm. In such spaces, the uniqueness of the solution is discussed and suitable conditions are determined to assure the stability and the convergence of the method. Several numerical tests are presented to show the efficiency of the method and the agreement with the theoretical estimates.
{"title":"A PROJECTION METHOD FOR VOLTERRA INTEGRAL EQUATIONS IN WEIGHTED SPACES OF CONTINUOUS FUNCTIONS","authors":"T. Diogo, L. Fermo, D. Occorsio","doi":"10.1216/jie.2022.34.433","DOIUrl":"https://doi.org/10.1216/jie.2022.34.433","url":null,"abstract":"A BSTRACT . This paper is concerned with the numerical treatment of second kind Volterra integral equations whose integrands present diagonal and/or endpoint algebraic singularities. A projection method based on an optimal interpolating operator is developed in the spaces of weighted continuous functions endowed with the supremum norm. In such spaces, the uniqueness of the solution is discussed and suitable conditions are determined to assure the stability and the convergence of the method. Several numerical tests are presented to show the efficiency of the method and the agreement with the theoretical estimates.","PeriodicalId":50176,"journal":{"name":"Journal of Integral Equations and Applications","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41663771","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"METHOD OF TIME-DISCRETIZATION TO A MULTITERM NONLINEAR RETARDED DIFFERENTIAL EQUATION","authors":"A. Khatoon, A. Raheem, A. Afreen","doi":"10.1216/jie.2022.34.449","DOIUrl":"https://doi.org/10.1216/jie.2022.34.449","url":null,"abstract":"","PeriodicalId":50176,"journal":{"name":"Journal of Integral Equations and Applications","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46311608","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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