Analysis and Mathematical Physics最新文献

In this paper, we consider a two-dimensional operator with an antisymmetric integral kernel, recently introduced by Z. Avetisyan and A. Karapetyants in connection to the study of general homogeneous operators. This is the unique two-dimensional operator that has an antisymmetric kernel homogeneous with respect to all orientation-preserving linear transformations of the plane. It is shown that the operator under consideration interacts naturally, both in Cartesian and polar coordinates, with projective tensor products of some classical functional spaces, such as Lebesgue, Hardy, and Hölder spaces; conditions for their boundedness as operators acting from these spaces to Banach lattices of measurable functions and estimates of their norms are given.

In this paper we give simple proofs for the main results concerning generalized Fekete-Szegő functional of type (left| a_{3}(f)-lambda a_{2}(f)^{2}right| -mu |a_{2}(f)|), where (lambda in mathbb {C}), (mu >0) and (a_{n}(f)) is n-th coefficient of the power series expansion of (fin mathcal {S}). In addition, we studied this functional separately for the class (mathcal {K}) of convex functions and we emphasize that all the results of the paper are sharp (i.e. the best possible). The advantages of the present study are that the techniques used in the proofs are more easier and use known results regarding the univalent functions, and those that it give the best possible results not only for the entire class of univalent normalized functions (mathcal {S}) but also for its subclass of convex functions (mathcal {K}).

We develop a new proof of the result of L.-E. Persson and V.D. Stepanov [24, Theorems 1 and 3], which provides a characterization of a Hardy integral inequality involving two weights, and which can be applied to an effective treatment of the geometric mean operator. Our approach enables us to extend their result to the full range of parameters, in particular involving the critical case (p=1), which was excluded in the original work. Our proof avoids all duality steps and discretization techniques and uses solely elementary means.

In this paper we provide insight into the classes of strongly subadditive/superadditive functions by highlighting numerous new examples and new results.

We find necessary and sufficient conditions on weights (u_1, u_2, v_1, v_2), i.e. measurable, positive, and finite, a.e. on (a, b), for which there exists a positive constant C such that for given (0< p_1,q_1,p_2,q_2 <infty ) the inequality

holds for every non-negative, measurable function f on (a, b), where (0 le a <b le infty ). The proof is based on a recently developed discretization method that enables us to overcome the restrictions of the earlier results.

We study a set of generalized V-line transforms, namely longitudinal, mixed, and transverse V-line transforms, of a symmetric m-tensor field in (mathbb {R}^2). The goal of this article is to recover a symmetric m-tensor field ({textbf {{f}}}) supported in a disk (mathbb {D}_R), with radius R and centered at the origin, by a combination of the aforementioned generalized V-line transforms, using two different techniques for different sets of data.

Sharp bounds are given for second Hankel determinant for the class of non-Bazilevic functions. We also give sharp bounds for the second Hankel determinant for the inverse and logarithmic inverse coefficients for this class of functions. Furthermore, non sharp bound for logarithmic coefficients is provided. Our results provide solution to long standing open problems for this class of functions.

The present work establishes sharp estimates for second-order Toeplitz determinant, given by (vert a_3^2 -a_4^2vert ), for the Ma-Minda class of starlike functions. These results are further extended to higher dimensions by deriving sharp bounds for a subclass of holomorphic mappings defined on the unit ball in a complex Banach space and the unit polydisc in (mathbb {C}^n), leading to corresponding estimates for second-order Toeplitz determinants for various subclasses of univalent mappings in several complex variables.

For suitable kernels on a locally compact space, we develop a theory of inner (outer) pseudo-balayage of quite general signed Radon measures (not necessarily of finite energy) onto quite general sets (not necessarily closed). Such investigations were initiated in Fuglede’s study (Anal. Math., 2016), which was, however, mainly concerned with the outer pseudo-balayage of positive measures of finite energy. The results thereby obtained solve Fuglede’s problem, posed to the author in a private correspondence (2016), whether his theory could be extended to measures of infinite energy. An application of this theory to weighted minimum energy problems is also given.

We propose two general methods for defining grand and small spaces based on Calderón’s construction and prove some fundamental properties of these spaces. In particular, we give a complete description of associative spaces to general grand and small spaces. Our description allows us to give an exact answer to the question posed in [25]. We give some examples illustrating our constructions for spaces constructed on sets of finite and infinite measure.