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.