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 H�LDER 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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“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)

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