This book presents a systematic treatment of generalized Orlicz spaces (also known as Musielak–Orlicz spaces) with minimal assumptions on the generating Φ-function. It introduces and develops a techni
This book is devoted exclusively to Lebesgue spaces and their direct derived spaces. Unique in its sole dedication, this book explores Lebesgue spaces, distribution functions and nonincreasing rearran
Several natural Lp spaces of analytic functions have been widely studied in the past few decades, including Hardy spaces, Bergman spaces, and Fock spaces. The terms “Hardy spaces” and “Bergman spaces”
Theory of Function Spaces II deals with the theory of function spaces of type Bspq and Fspq as it stands at the present. These two scales of spaces cover many well-known function spaces such as Holder
Learning spaces offer a rigorous mathematical foundation for practical systems of educational technology. Learning spaces generalize partially ordered sets and are special cases of knowledge spaces. T
This volume provides a complete introduction to metric space theory. It covers the topology of metric spaces, continuity, connectedness, compactness and product spaces, and includes results such as th
Several books deal with Sobolev spaces on open subsets of R (n), but none yet with Sobolev spaces on Riemannian manifolds, despite the fact that the theory of Sobolev spaces on Riemannian manifolds al
This monograph summarizes the recent major achievements in Möbius invariant QK spaces. First introduced by Hasi Wulan and his collaborators, the theory of QK spaces has developed immensely in the last
The present volume develops the theory of integration in Banach spaces, martingales and UMD spaces, and culminates in a treatment of the Hilbert transform, Littlewood-Paley theory and the vector-value
Key definitions and results in symmetric spaces, particularly Lp, Lorentz, Marcinkiewicz and Orlicz spaces are emphasized in this textbook. A comprehensive overview of the Lorentz, Marcinkiewicz and O
This text is an introduction to harmonic analysis on symmetric spaces, focusing on advanced topics such as higher rank spaces, positive definite matrix space and generalizations. It is intended for be
Written by a team of leading experts in the field, this volume presents a self-contained account of the theory, techniques and results in metric type spaces (in particular in G-metric spaces); that is
Systematically constructing an optimal theory, this monograph develops and explores several approaches to Hardy spaces in the setting of Alhlfors-regular quasi-metric spaces. The text is divided into
This monograph provides a concise introduction to the main results and methods of the fixed point theory in modular function spaces. Modular function spaces are natural generalizations of both functio
Classical Sobolev spaces, based on Lebesgue spaces on an underlying domain with smooth boundary, are not only of considerable intrinsic interest but have for many years proved to be indispensible in t
This book surveys the development of integral geometry on domains of homogeneous spaces, covering analysis of multidimensional Euclidean domains and Riemannian symmetric spaces of arbitrary ranks as w
In the current panorama of urban growth and planning in many urban territories of western societies, open spaces are residual spaces of urban occupation or are reserved for eventual occupation. Open s
The theory of elliptic boundary problems is fundamental in analysis and the role of spaces of weakly differentiable functions (also called Sobolev spaces) is essential in this theory as a tool for ana
Sobolev spaces play an outstanding role in modern analysis, in particular, in the theory of partial differential equations and its applications in mathematical physics. They form an indispensable tool
The fundamental contributions of Professor Maz'ya to the theory of function spaces and especially Sobolev spaces are well known and often play a key role in the study of different aspects of the theor
Historically, for metric spaces the quest for universal spaces in dimension theory spanned approximately a century of mathematical research. The history breaks naturally into two periods - the classi
Sobolev spaces become the established and universal language of partial differential equations and mathematical analysis. Among a huge variety of problems where Sobolev spaces are used, the following
The abstract concepts of metric spaces are often perceived as difficult. This book offers a unique approach to the subject which gives readers the advantage of a new perspective on ideas familiar from
Classical Sobolev spaces, based on Lebesgue spaces on an underlying domain with smooth boundary, are not only of considerable intrinsic interest but have for many years proved to be indispensible in t
This book deals with the geometrical structure of finite dimensional normed spaces, as the dimension grows to infinity. This is a part of what came to be known as the Local Theory of Banach Spaces (th
A description of the global properties of simply-connected spaces that are non-positively curved in the sense of A. D. Alexandrov, and the structure of groups which act on such spaces by isometries. T
This book establishes the foundations of the theory of bounded and unbounded weighted composition operators in L²-spaces. It develops the theory in full generality, meaning that the corresponding comp
This book presents a comprehensive account of the theory of spaces of continuous functions under uniform, fine and graph topologies. Besides giving full details of known results, an attempt is made to
This monograph is devoted to the study of spear operators, that is, bounded linear operators $G$ between Banach spaces $X$ and $Y$ satisfying that for every other bounded linear operator $T:X\longrigh
This integrated collection of perspectives on the spaces of teaching and learning uses ‘learning space’ to place educational practice in context. It considers the complex relationships involved in the
This second volume of Analysis in Banach Spaces, Probabilistic Methods and Operator Theory, is the successor to Volume I, Martingales and Littlewood-Paley Theory. It presents a thorough study of the f
This book gives a compact exposition of the fundamentals of the theory of locally convex topological vector spaces. Furthermore it contains a survey of the most important results of a more subtle natu
The main purpose of this book is to give a detailed and complete survey of recent progress related to the real-variable theory of Musielak–Orlicz Hardy-type function spaces, and to lay the foundations
The book presents an introduction to the geometry of Hilbert spaces and operator theory, targeting graduate and senior undergraduate students of mathematics. Major topics discussed in the book are inn
This is an collection of some easily-formulated problems that remain open in the study of the geometry and analysis of Banach spaces. Assuming the reader has a working familiarity with the basic resul
This monograph contains a detailed exposition of the up-to-date theory of separably injective spaces: new and old results are put into perspective with concrete examples (such as\ell_\infty/c_0 and C(
Aimed toward researchers and graduate students familiar with elements of functional analysis, linear algebra, and general topology; this book contains a general study of modulars, modular spaces, and
This third volume in Vladimir Tkachuk's series on Cp-theory problems applies all modern methods of Cp-theory to study compactness-like properties in function spaces and introduces the reader to the th
This book, which is based on several courses of lectures given by the author at the Independent University of Moscow, is devoted to Sobolev-type spaces and boundary value problems for linear elliptic
