BOUNDEDNESS OF RIEMANN-LIOUVILLE OPERATOR FROM WEIGHTED SOBOLEV SPACE TO WEIGHTED LEBESGUE SPACE

IF 0.6 Q3 MATHEMATICS Eurasian Mathematical Journal Pub Date : 2021-01-01 DOI:10.32523/2077-9879-2021-12-1-39-48

A. Kalybay, R. Oinarov

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引用次数: 3

Abstract

References: [1] A. ABYLAYEVA, R. OINAROV ANDL.-E. PERSSON, Boundedness and compactness of a class of Hardy type operators, J. Ineq. Appl. 2016, 324 (2016), https://doi.org/10.1186/s13660-016-1266-y. · Zbl 1351.26009 [2] L. ARENDARENKO, Estimates for Hardy-type integral operators in weighted Lebesgue spaces, Doctoral Thesis, Lule ̊a University of Technology, 2013. [3] E. N. BATUEV ANDV. D. STEPANOV, Weighted inequalities of Hardy type, Siberian Math. J. 30, 1 (1989), 8-16. · Zbl 0729.42007 [4] T. CHEN ANDG. SINNAMON, Generalized Hardy operators and normalizing measures, J. Ineq. Appl. 7, (2002), 829-866. · Zbl 1068.42018 [5] A. GOGATISHVILI ANDJ. LANG, The generalized Hardy operators with kernel and variable integral limits in Banach function spaces, J. Ineq. Appl. 4, (1999), 1-16. [6] H. P. HEINING ANDG. SINNAMON, Mapping properties of integral averaging operators, Stud. Math. 129, (1998), 157-177. · Zbl 0910.26008 [7] A. A. KALYBAY ANDR. OINAROV, Kernel operators and their boundedness from weighted Sobolev space to weighted Lebesgue space, Turk. J. Math. 43, (2019), 301-315. · Zbl 07052290 [8] A. A. KALYBAY ANDR. OINAROV, Boundedness of Riemann-Liouville operator from weighted Sobolev space to weighted Lebesgue space, Eurasian Math. J. 12, 1 (2021), 39-48. · Zbl 1474.26067 [9] A. KUFNER, L. MALIGRANDA ANDL.-E. PERSSON, The Hardy Inequality. About its history and some related results, Vydavatelsk ́y servis, Pilsen, 2007. [10] A. A. MESKHI, Solution of some weight problems for the Riemann-Liouville and Weyl operators, Georgian Math. J., 5, 6 (1998), 565-574. · Zbl 0931.42008 [11] R. OINAROV, On weighted norm inequalities with three weights, J. London Math. Soc. 48, 2 (1993), 103-116. · Zbl 0811.26008 [12] R. OINAROV, Boundedness of integral operators from weighted Sobolev space to weighted Lebesgue space, Complex Var. Elliptic Equ. 56, 10-11 (2011), 1021-1038. · Zbl 1226.26013 [13] R. OINAROV, Boundedness of integral operators in weighted Sobolev spaces, Izv. Math. 78, 4 (2014), 836-853. · Zbl 1305.47032 [14] R. OINAROV, Boundedness and compactness of Volterra type integral operators, Siberian Math. J. 48, 5 (2007), 884-896. · Zbl 1164.47346 [15] R. OINAROV, Boundedness and compactness in weighted Lebesgue spaces of integral operators with variable integration limits, Siberian Math. J., 52, 6 (2011), 1042-1055. · Zbl 1237.47051 [16] R. OINAROV ANDM. OTELBAEV, A criterion for the discreteness of the spectrum of the general Sturm-Liouville operator, and embedding theorems connected with it, Differ. Equ. 24, 4 (1988), 402408. · Zbl 0673.34027 [17] D. V. PROKHOROV, On the boundedness and compactness of a class of integral operators, J. London Math. Soc. 64, 2 (2000), 617-628. · Zbl 0956.47019 [18] D. V. PROKHOROV ANDV. D. STEPANOV, Weighted estimates for the Riemann-Liouville operators and applications, Proc. Steklov Inst. Math. 243, (2003), 278-301. · Zbl 1081.26004

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riemann-liouville算子从加权sobolev空间到加权lebesgue空间的有界性

参考文献:A. ABYLAYEVA, R. ininarov, l .- e。一类Hardy型算子的紧性与有界性，J. Ineq。苹果，2016,324 (2016)，https://doi.org/10.1186/s13660-016-1266-y。·Zbl 1351.26009 bbbl . ARENDARENKO，加权Lebesgue空间中hardy型积分算子的估计，博士论文，黑龙江理工大学，2013。b[3] e. n.巴图夫和v .;D. STEPANOV, Hardy型加权不等式，西伯利亚数学。[j] .科学通报，1(1989)，8-16。·[Zbl] 0729.42007[[4]]陈德刚。辛纳蒙，广义Hardy算子与规格化测度，[j]。应用科学7，(2002)，829-866。·Zbl 1068.42018 [5] A. GOGATISHVILI ANDJ.;王志强，具有核和变积分极限的广义Hardy算子，在Banach函数空间，j。应用学报，(1999)，1-16。b[6] h. p.海宁和。积分平均算子的映射性质，第2章。数学。129，(1998)，157-177。·Zbl 0910.26008 [7] a.a. KALYBAY ANDR从加权Sobolev空间到加权Lebesgue空间的核算子及其有界性，土耳其文。数学学报，43(2019)，301-315。·Zbl 07052290 [8] a.a. KALYBAY ANDRininarov，从加权Sobolev空间到加权Lebesgue空间的Riemann-Liouville算子的有界性，欧亚数学。J.学报，1(2021)，39-48。·Zbl 1474.26067 bbb A. KUFNER, L. MALIGRANDA和L.- e。《哈代不等式》。关于它的历史和一些相关的结果，Vydavatelsk ø y servis, Pilsen, 2007。[10] A. A. MESKHI, Riemann-Liouville和Weyl算子的一些权问题的解，数学。[J] .， 5, 6(1998)， 565-574。·[j]李彦宏，关于三权值的加权范数不等式，数学学报(自然科学版)。社会法学，48(1993)，103-116。·Zbl 0811.26008 bbb R. ininarov，从加权Sobolev空间到加权Lebesgue空间的积分算子的有界性，复变方程，56,10-11(2011)，1021-1038。·R. ininarov，加权Sobolev空间中积分算子的有界性，vol . 11 - 12数学。78,4(2014)，836-853。·R. ininarov, Volterra型积分算子的紧性和有界性，数学学报，2001,11(5):557 - 557。[j] .生物医学工程学报，2007,31(2):389 - 396。·Zbl [1] R. ininarov，具有变积分极限的积分算子在Lebesgue空间中的有界性和紧性，数学学报。[J] .生物医学工程学报，2011,26(6):1042-1055。·Zbl 123747051 bb0 R. ininarov ANDM。一般Sturm-Liouville算子谱离散性的判据，以及与之相关的嵌入定理。方程24,4(1988)，402408。·J. D. V. PROKHOROV，一类积分算子的紧性和有界性，数学学报。社会科学学报，2(2000)，617-628。·Zbl 0956.47019 [18] D. V. PROKHOROV等。D. STEPANOV, Riemann-Liouville算子的加权估计及其应用，数学学报，43(2003)，278-301。·Zbl 1081.26004

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Eurasian Mathematical Journal MATHEMATICS-

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期刊介绍： Publication of carefully selected original research papers in all areas of mathematics written by mathematicians first of all from Europe and Asia. However papers by mathematicians from other continents are also welcome. From time to time Eurasian Mathematical Journal will also publish survey papers.

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