Inequalities and Integral Operators in Function Spaces

Erlan Nursultanov

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English

CRC Press
27 January 2026

Functional analysis & transforms; Geometry

Series: Chapman & Hall/CRC Monographs and Research Notes in Mathematics

The modern theory of functional spaces and operators, built on powerful analytical methods, continues to evolve in the search for more precise, universal, and effective tools. Classical inequalities such as Hardy’s inequality, Remez’s inequality, the Bernstein-Nikolsky inequality, the Hardy-Littlewood-Sobolev inequality for the Riesz transform, the Hardy-Littlewood inequality for Fourier transforms, O’Neil’s inequality for the convolution operator, and others play a fundamental role in analysis, and their influence is hard to overestimate. With the development of new interpolation methods, new functional spaces, and novel problem formulations for functions of many variables, these inequalities have undergone significant advancements.

Inequalities and Integral Operators in Function Spaces focuses primarily on new approaches to the interpolation of spaces, which significantly extend the classical framework of the methods developed by Lions and Peetre. The book demonstrates how the use of net spaces and modern interpolation techniques not only provides a deeper understanding of the structure of functional spaces but also leads to stronger results that cannot be achieved within the traditional framework.

Features:

Can be used for specialized courses in harmonic analysis focusing on interpolation Suitable for both researchers in the field of real analysis and mathematicians interested in applying these methods to related areas Contains new and interesting results, previously unpublished

By: Erlan Nursultanov
Imprint: CRC Press
Country of Publication: United Kingdom
Dimensions: Height: 234mm, Width: 156mm,
ISBN: 9781041126843
ISBN 10: 1041126840
Series: Chapman & Hall/CRC Monographs and Research Notes in Mathematics
Pages: 306
Publication Date: 27 January 2026
Audience: College/higher education , Professional and scholarly , Further / Higher Education , Undergraduate
Format: Hardback
Publisher's Status: Forthcoming

Foreword Preface 1 Inequalities related to permutations of functions 2 Multiparameter interpolation method 3 Interpolation method for spaces with mixed metric 4 Interpolation theorems for integral operators 5 Nikolsky’s inequalities 6 Remez inequalities 7 Hardy-Littlewood inequalities for trigonometric series 8 Stein inequalities for the Fourier transform 9 Net spaces and Nursultanov inequalities 10 Weighted norm inequalities for Fourier transforms 11 O’Neil inequalities 12 Weighted norm inequalities for convolution and Riesz potential13 O’Neil inequalities on Morrey spaces14 Interpolation theorems for nonlinear integral operators Bibliography Index

Erlan Nursultanov is a Doctor of Physical and Mathematical Sciences and a Professor at the Kazakhstan Branch of Lomonosov Moscow State University. He graduated from the Faculty of Mathematics at Karaganda State University in 1979 and completed his postgraduate studies at the Faculty of Mechanics and Mathematics of Moscow State University in 1982. He received his PhD in Mathematics in 1983 (MSU) and his Doctor of Sciences degree in 1999 from the Steklov Mathematical Institute of the Russian Academy of Sciences. His research interests include harmonic analysis, operator theory, interpolation of function spaces, and approximation theory. He is the author of over 100 scientific publications.