Classical and Multidimensional Lorentz Spaces

Classical and Multidimensional Lorentz Spaces
Author: René Erlin Castillo
Publisher: Walter de Gruyter GmbH & Co KG
Total Pages: 204
Release: 2021-09-07
Genre: Mathematics
ISBN: 311075035X

This work is solely dedicated to the study of both the one variable as well as the multidimensional Lorentz spaces covering the theory of Lebesgue type spaces invariant by rearrangement. The authors provide proofs in full detail for most theorems. The self-contained text is valuable for advanced students and researchers.

Classical and Multidimensional Lorentz Spaces

Classical and Multidimensional Lorentz Spaces
Author: René Erlin Castillo
Publisher: Walter de Gruyter GmbH & Co KG
Total Pages: 152
Release: 2021-09-07
Genre: Mathematics
ISBN: 3110750376

This work is solely dedicated to the study of both the one variable as well as the multidimensional Lorentz spaces covering the theory of Lebesgue type spaces invariant by rearrangement. The authors provide proofs in full detail for most theorems. The self-contained text is valuable for advanced students and researchers.

Multidimensional Geographic Information Science

Multidimensional Geographic Information Science
Author: Jonathan Raper
Publisher: CRC Press
Total Pages: 336
Release: 2000-11-23
Genre: Technology & Engineering
ISBN: 0203301226

The way people normally view a GIS is 2-dimensional, a greatly limiting form. However, as developments occur within the field, researchers and practitioners are finding ways to make a GIS 3-dimensional, and in some instances even 4-dimensional. Being able to view a GIS in more than 2 dimensions greatly enhances its usability. This forward-lookin

Classical Fourier Analysis

Classical Fourier Analysis
Author: Loukas Grafakos
Publisher: Springer
Total Pages: 647
Release: 2014-11-17
Genre: Mathematics
ISBN: 1493911945

The main goal of this text is to present the theoretical foundation of the field of Fourier analysis on Euclidean spaces. It covers classical topics such as interpolation, Fourier series, the Fourier transform, maximal functions, singular integrals, and Littlewood–Paley theory. The primary readership is intended to be graduate students in mathematics with the prerequisite including satisfactory completion of courses in real and complex variables. The coverage of topics and exposition style are designed to leave no gaps in understanding and stimulate further study. This third edition includes new Sections 3.5, 4.4, 4.5 as well as a new chapter on “Weighted Inequalities,” which has been moved from GTM 250, 2nd Edition. Appendices I and B.9 are also new to this edition. Countless corrections and improvements have been made to the material from the second edition. Additions and improvements include: more examples and applications, new and more relevant hints for the existing exercises, new exercises, and improved references.

Function Spaces, 1

Function Spaces, 1
Author: Luboš Pick
Publisher: Walter de Gruyter
Total Pages: 495
Release: 2012-12-19
Genre: Mathematics
ISBN: 311025042X

This is the first part of the second revised and extended edition of the well established book "Function Spaces" by Alois Kufner, Oldřich John, and Svatopluk Fučík. Like the first edition this monograph is an introduction to function spaces defined in terms of differentiability and integrability classes. It provides a catalogue of various spaces and benefits as a handbook for those who use function spaces in their research or lecture courses. This first volume is devoted to the study of function spaces, based on intrinsic properties of a function such as its size, continuity, smoothness, various forms of a control over the mean oscillation, and so on. The second volume will be dedicated to the study of function spaces of Sobolev type, in which the key notion is the weak derivative of a function of several variables.

Weighted Inequalities Of Hardy Type (Second Edition)

Weighted Inequalities Of Hardy Type (Second Edition)
Author: Lars-erik Persson
Publisher: World Scientific Publishing Company
Total Pages: 480
Release: 2017-06-16
Genre: Mathematics
ISBN: 9813140666

Inequalities play an important role in almost all branches of mathematics as well as in other areas of science and engineering. This book surveys the present state of the theory of weighted integral inequalities of Hardy type, including modifications concerning Hardy-Steklov operators, and some basic results about Hardy-type inequalities and their limit (Carleman-Knopp type) inequalities. It also describes some rather new areas such as higher order and fractional order Hardy-type inequalities and integral inequalities on the cone of monotone functions, together with some applications and open problems.In this second edition, all chapters in the first edition have been updated with new information. Moreover, a new chapter contains new and complementary information concerning: (a) a convexity approach to prove and explain Hardy-type inequalities; (b) sharp constants; (c) scales of inequalities to characterize Hardy-type inequalities; (d) Hardy-type inequalities in other function spaces; and (e) a number of new open questions.

Multidimensional Analysis and Discrete Models

Multidimensional Analysis and Discrete Models
Author: Aleksei A. Dezin
Publisher: CRC Press
Total Pages: 188
Release: 2018-01-18
Genre: Mathematics
ISBN: 135109176X

Multidimensional Analysis and Discrete Models, a thorough and detailed reference, covers the main structures of multidimensional analysis and the intrinsically defined discrete models in applied mathematics, mathematical physics, and related fields. The material is presented in a clear and straightforward manner, with background information provided to define finite models and to clarify the concepts of multidimensional analysis. The book covers special difference models of the mathematical physics equations, models of boundary value problems, and objects of quantum mechanics. Considerable attention is also given to differential operators on Riemannian manifolds and the interpretation of classical vector analysis. The primary focus of Multidimensional Analysis and Discrete Models is on the description of regular methods of constructing intrinsically defined discrete models for special classes of continual objects, but emphasis is also given to the interaction of ideas and methods that exist throughout the field of mathematics. For example, the connections between theories derived from classical and functional analysis, Riemannian geometry, and algebraic topology are illustrated, and are discussed in terms of their relevance to computing solutions.