Hardy Operators, Function Spaces and Embeddings
Author: David E Edmunds
Publisher: Springer
Published: 2014-01-15
Total Pages: 344
ISBN-13: 9783662077320
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Hardy Operators, Function Spaces and Embeddings
Author: David E. Edmunds
Publisher: Springer Science & Business Media
Published: 2013-03-09
Total Pages: 334
ISBN-13: 3662077310
DOWNLOAD EBOOKClassical 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 the study of partial differential equations and variational problems. Many developments of the basic theory since its inception arise in response to concrete problems, for example, with the (ubiquitous) sets with fractal boundaries. The theory will probably enjoy substantial further growth, but even now a connected account of the mature parts of it makes a useful addition to the literature. Accordingly, the main themes of this book are Banach spaces and spaces of Sobolev type based on them; integral operators of Hardy type on intervals and on trees; and the distribution of the approximation numbers (singular numbers in the Hilbert space case) of embeddings of Sobolev spaces based on generalised ridged domains. This timely book will be of interest to all those concerned with the partial differential equations and their ramifications. A prerequisite for reading it is a good graduate course in real analysis.
Function Spaces of Logarithmic Smoothness: Embeddings and Characterizations
Author: Óscar Domínguez
Publisher: American Mathematical Society
Published: 2023-02-13
Total Pages: 180
ISBN-13: 1470455382
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Eigenvalues, Embeddings and Generalised Trigonometric Functions
Author: Jan Lang
Publisher: Springer Science & Business Media
Published: 2011-03-23
Total Pages: 232
ISBN-13: 3642182674
DOWNLOAD EBOOKThe main theme of the book is the study, from the standpoint of s-numbers, of integral operators of Hardy type and related Sobolev embeddings. In the theory of s-numbers the idea is to attach to every bounded linear map between Banach spaces a monotone decreasing sequence of non-negative numbers with a view to the classification of operators according to the way in which these numbers approach a limit: approximation numbers provide an especially important example of such numbers. The asymptotic behavior of the s-numbers of Hardy operators acting between Lebesgue spaces is determined here in a wide variety of cases. The proof methods involve the geometry of Banach spaces and generalized trigonometric functions; there are connections with the theory of the p-Laplacian.
Fractional Sobolev Spaces and Inequalities
Author: D. E. Edmunds
Publisher: Cambridge University Press
Published: 2022-10-31
Total Pages: 169
ISBN-13: 1009254634
DOWNLOAD EBOOKProvides an account of fractional Sobolev spaces emphasising applications to famous inequalities. Ideal for graduates and researchers.
Spectral Theory, Function Spaces and Inequalities
Author: B. Malcolm Brown
Publisher: Springer Science & Business Media
Published: 2011-11-06
Total Pages: 269
ISBN-13: 3034802633
DOWNLOAD EBOOKThis is a collection of contributed papers which focus on recent results in areas of differential equations, function spaces, operator theory and interpolation theory. In particular, it covers current work on measures of non-compactness and real interpolation, sharp Hardy-Littlewood-Sobolev inequalites, the HELP inequality, error estimates and spectral theory of elliptic operators, pseudo differential operators with discontinuous symbols, variable exponent spaces and entropy numbers. These papers contribute to areas of analysis which have been and continue to be heavily influenced by the leading British analysts David Edmunds and Des Evans. This book marks their respective 80th and 70th birthdays.
Function Spaces and Inequalities
Author: Pankaj Jain
Publisher: Springer
Published: 2017-10-20
Total Pages: 334
ISBN-13: 981106119X
DOWNLOAD EBOOKThis book features original research and survey articles on the topics of function spaces and inequalities. It focuses on (variable/grand/small) Lebesgue spaces, Orlicz spaces, Lorentz spaces, and Morrey spaces and deals with mapping properties of operators, (weighted) inequalities, pointwise multipliers and interpolation. Moreover, it considers Sobolev–Besov and Triebel–Lizorkin type smoothness spaces. The book includes papers by leading international researchers, presented at the International Conference on Function Spaces and Inequalities, held at the South Asian University, New Delhi, India, on 11–15 December 2015, which focused on recent developments in the theory of spaces with variable exponents. It also offers further investigations concerning Sobolev-type embeddings, discrete inequalities and harmonic analysis. Each chapter is dedicated to a specific topic and written by leading experts, providing an overview of the subject and stimulating future research.
Integral Operators in Non-Standard Function Spaces
Author: Vakhtang Kokilashvili
Publisher: Birkhäuser
Published: 2016-05-11
Total Pages: 585
ISBN-13: 3319210157
DOWNLOAD EBOOKThis book, the result of the authors' long and fruitful collaboration, focuses on integral operators in new, non-standard function spaces and presents a systematic study of the boundedness and compactness properties of basic, harmonic analysis integral operators in the following function spaces, among others: variable exponent Lebesgue and amalgam spaces, variable Hölder spaces, variable exponent Campanato, Morrey and Herz spaces, Iwaniec-Sbordone (grand Lebesgue) spaces, grand variable exponent Lebesgue spaces unifying the two spaces mentioned above, grand Morrey spaces, generalized grand Morrey spaces, and weighted analogues of some of them. The results obtained are widely applied to non-linear PDEs, singular integrals and PDO theory. One of the book's most distinctive features is that the majority of the statements proved here are in the form of criteria. The book is intended for a broad audience, ranging from researchers in the area to experts in applied mathematics and prospective students.
Analysis on Function Spaces of Musielak-Orlicz Type
Author: Osvaldo Mendez
Publisher: CRC Press
Published: 2019-01-21
Total Pages: 262
ISBN-13: 0429524102
DOWNLOAD EBOOKAnalysis on Function Spaces of Musielak-Orlicz Type provides a state-of-the-art survey on the theory of function spaces of Musielak-Orlicz type. The book also offers readers a step-by-step introduction to the theory of Musielak–Orlicz spaces, and introduces associated function spaces, extending up to the current research on the topic Musielak-Orlicz spaces came under renewed interest when applications to electrorheological hydrodynamics forced the particular case of the variable exponent Lebesgue spaces on to center stage. Since then, research efforts have typically been oriented towards carrying over the results of classical analysis into the framework of variable exponent function spaces. In recent years it has been suggested that many of the fundamental results in the realm of variable exponent Lebesgue spaces depend only on the intrinsic structure of the Musielak-Orlicz function, thus opening the door for a unified theory which encompasses that of Lebesgue function spaces with variable exponent. Features Gives a self-contained, concise account of the basic theory, in such a way that even early-stage graduate students will find it useful Contains numerous applications Facilitates the unified treatment of seemingly different theoretical and applied problems Includes a number of open problems in the area
Spectral Theory and Differential Operators
Author: David Eric Edmunds
Publisher: Oxford University Press
Published: 2018
Total Pages: 610
ISBN-13: 0198812051
DOWNLOAD EBOOKThis book is an updated version of the classic 1987 monograph "Spectral Theory and Differential Operators".The original book was a cutting edge account of the theory of bounded and closed linear operators in Banach and Hilbert spaces relevant to spectral problems involving differential equations. It is accessible to a graduate student as well as meeting the needs of seasoned researchers in mathematics and mathematical physics. This revised edition corrects various errors, and adds extensive notes to the end of each chapter which describe the considerable progress that has been made on the topic in the last 30 years.
