Variable Lebesgue Spaces - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Variable Lebesgue Spaces write by David V. Cruz-Uribe. This book was released on 2013-02-12. Variable Lebesgue Spaces available in PDF, EPUB and Kindle. This book provides an accessible introduction to the theory of variable Lebesgue spaces. These spaces generalize the classical Lebesgue spaces by replacing the constant exponent p with a variable exponent p(x). They were introduced in the early 1930s but have become the focus of renewed interest since the early 1990s because of their connection with the calculus of variations and partial differential equations with nonstandard growth conditions, and for their applications to problems in physics and image processing. The book begins with the development of the basic function space properties. It avoids a more abstract, functional analysis approach, instead emphasizing an hands-on approach that makes clear the similarities and differences between the variable and classical Lebesgue spaces. The subsequent chapters are devoted to harmonic analysis on variable Lebesgue spaces. The theory of the Hardy-Littlewood maximal operator is completely developed, and the connections between variable Lebesgue spaces and the weighted norm inequalities are introduced. The other important operators in harmonic analysis - singular integrals, Riesz potentials, and approximate identities - are treated using a powerful generalization of the Rubio de Francia theory of extrapolation from the theory of weighted norm inequalities. The final chapter applies the results from previous chapters to prove basic results about variable Sobolev spaces.
Lebesgue and Sobolev Spaces with Variable Exponents
Lebesgue and Sobolev Spaces with Variable Exponents - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Lebesgue and Sobolev Spaces with Variable Exponents write by Lars Diening. This book was released on 2011-03-29. Lebesgue and Sobolev Spaces with Variable Exponents available in PDF, EPUB and Kindle. The field of variable exponent function spaces has witnessed an explosive growth in recent years. The standard reference article for basic properties is already 20 years old. Thus this self-contained monograph collecting all the basic properties of variable exponent Lebesgue and Sobolev spaces is timely and provides a much-needed accessible reference work utilizing consistent notation and terminology. Many results are also provided with new and improved proofs. The book also presents a number of applications to PDE and fluid dynamics.
An Introductory Course in Lebesgue Spaces
An Introductory Course in Lebesgue Spaces - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook An Introductory Course in Lebesgue Spaces write by Rene Erlin Castillo. This book was released on 2016-06-23. An Introductory Course in Lebesgue Spaces available in PDF, EPUB and Kindle. 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 rearrangement. Moreover, it also deals with weak, Lorentz and the more recent variable exponent and grand Lebesgue spaces with considerable detail to the proofs. The book also touches on basic harmonic analysis in the aforementioned spaces. An appendix is given at the end of the book giving it a self-contained character. This work is ideal for teachers, graduate students and researchers.
Variable Lebesgue Spaces
Variable Lebesgue Spaces - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Variable Lebesgue Spaces write by Springer. This book was released on 2013-02-12. Variable Lebesgue Spaces available in PDF, EPUB and Kindle.
Lebesgue and Sobolev Spaces with Variable Exponents
Lebesgue and Sobolev Spaces with Variable Exponents - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Lebesgue and Sobolev Spaces with Variable Exponents write by Lars Diening. This book was released on 2011-03-31. Lebesgue and Sobolev Spaces with Variable Exponents available in PDF, EPUB and Kindle. The field of variable exponent function spaces has witnessed an explosive growth in recent years. The standard reference article for basic properties is already 20 years old. Thus this self-contained monograph collecting all the basic properties of variable exponent Lebesgue and Sobolev spaces is timely and provides a much-needed accessible reference work utilizing consistent notation and terminology. Many results are also provided with new and improved proofs. The book also presents a number of applications to PDE and fluid dynamics.
