The survey is aimed at providing detailed information about recent results in the problem of the boundedness in general Morrey-type spaces of various important operators of real analysis, namely of the maximal operator, fractional maximal operator, Riesz potential, singular integral operator, Hardy operator. The main focus is on the results which contain, for a certain range of the numerical parameters, necessary and sufficient conditions on the functional parameters characterizing general Morrey-type spaces, ensuring the boundedness of the aforementioned operators from one general Morrey-type space to another one. The major part of the survey is dedicated to the results obtained by the author jointly with his co-authores A. Gogatishvili, M. L. Goldman, D. K. Darbayeva, H. V. Guliyev, V. S. Guliyev, P. Jain, R. Mustafaev, E. D. Nursultanov, R. Oinarov, A. Serbetci, T. V. Tararykova. In Part I of the survey under discussion were the definition and basic properties of the local and global general Morrey-type spaces, embedding theorems, and the boundedness properties of the maximal operator. Part II of the survey contains discussion of boundedness properties of the fractional maximal operator, Riesz potential, singular integral operator, Hardy operator. All definitions and notation in Part II are the same as in Part I.

Authors

Burenkov V.I.
^{1}

Journal

Publisher

Eurasian Mathematical Journal

Language

English

Pages

21-45

Status

Published

Number

1

Volume

4

Year

2013

Organizations

^{1}Peoples’ Friendship University of Russia

Keywords

local and global Morrey-type spaces; fractional maximal operator; Riesz potential; singular integral operator; Hardy operator

Date of creation

20.07.2021

Date of change

20.07.2021

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