Integral Operators in Non-Standard Function Spaces

Volume 2: Variable Exponent Hölder, Morrey–Campanato and Grand Spaces

Vakhtang Kokilashvili, Alexander Meskhi, Humberto Rafeiro, Stefan Samko (Autoren)

Buch | Hardcover

XXIII, 434 Seiten

2016 | 1st ed. 2016
Springer International Publishing (Verlag)
978-3-319-21017-9 (ISBN)

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This 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.

IV: Grand Lebesgue Spaces.- 14 Maximal Functions and Potentials.- 15 Grand Lebesgue Spaces on Sets with Infinite Measure.- V: Grand Morrey Spaces.- 16 Maximal Functions, Fractional and Singular Integrals.- 17 Multiple Operators on the Cone of Decreasing Functions.- A: Grand Bochner Spaces.- Bibliography.- Symbol Index.- Subject Index.IV: Grand Lebesgue Spaces.- 14 Maximal Functions and Potentials.- 15 Grand Lebesgue Spaces on Sets with Infinite Measure.- V: Grand Morrey Spaces.- 16 Maximal Functions, Fractional and Singular Integrals.- 17 Multiple Operators on the Cone of Decreasing Functions.- A: Grand Bochner Spaces.- Bibliography.- Symbol Index.- Subject Index.

"The entire book, which is written in a complete consecutive way of presentation of the material, could be considered as a short encyclopedia, very useful for providing a basis for further research in the area." (Nikos Labropoulos, Mathematical Reviews, August, 2017)

Erscheint lt. Verlag	23.5.2016
Reihe/Serie	Operator Theory: Advances and Applications
Zusatzinfo	XXIII, 434 p.
Verlagsort	Cham
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
Schlagworte	commutators • Compactness • grand Bochner spaces • grand Lebesgue spaces • grand Morrey spaces • grand variable exponent Lebesgue spaces • maximal, singular and potential operators • Morrey-Campanato and Herz spaces • Morrey spaces • product kernels • Sobolev-type theorem • variable exponent Hölder spaces • variable exponent Morrey spaces • variable Herz spaces
ISBN-10	3-319-21017-3 / 3319210173
ISBN-13	978-3-319-21017-9 / 9783319210179
Zustand	Neuware