Integral Operators in Non-Standard Function Spaces

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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.<p>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.</p><p>The book is intended for a broad audience, ranging from researchers in the area to experts in applied mathematics and prospective students.</p>

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