Kokilashvili V., Meskhi A., Rafeiro H., Samko S. Integral Operators in Non-Standard Function Spaces. Volume 2: Variable Exponent Hölder, Morrey-Campanato and Grand Spaces

Basel: Birkhäuser, 2016. — 1003 p. — (Operator Theory: Advances and Applications 249). — ISBN: 978-3-319-21018-6; 978-3-319-21017-9.​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.Variable Exponent Hölder Spaces
Morrey and Stummel Spaces with Constant Exponents
Morrey, Campanato and Herz Spaces with Variable Exponents
Singular Integrals and Potentials in Grand Lebesgue Spaces
Grand Lebesgue Spaces on Sets of Infinite Measure
Fractional and Singular Integrals in Grand Morrey Spaces
Multivariable Operators on the Cone of Decreasing Functions