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Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Integral equations
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Bounded and Compact Integral Operators (Paperback, Softcover reprint of hardcover 1st ed. 2002)
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Bounded and Compact Integral Operators (Paperback, Softcover reprint of hardcover 1st ed. 2002)
Series: Mathematics and Its Applications, 543
Expected to ship within 10 - 15 working days
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The monograph presents some of the authors' recent and original
results concerning boundedness and compactness problems in Banach
function spaces both for classical operators and integral
transforms defined, generally speaking, on nonhomogeneous spaces.
Itfocuses onintegral operators naturally arising in boundary value
problems for PDE, the spectral theory of differential operators,
continuum and quantum mechanics, stochastic processes etc. The book
may be considered as a systematic and detailed analysis of a large
class of specific integral operators from the boundedness and
compactness point of view. A characteristic feature of the
monograph is that most of the statements proved here have the form
of criteria. These criteria enable us, for example, togive var ious
explicit examples of pairs of weighted Banach function spaces
governing boundedness/compactness of a wide class of integral
operators. The book has two main parts. The first part, consisting
of Chapters 1-5, covers theinvestigation ofclassical operators:
Hardy-type transforms, fractional integrals, potentials and maximal
functions. Our main goal is to give a complete description of those
Banach function spaces in which the above-mentioned operators act
boundedly (com pactly). When a given operator is not bounded
(compact), for example in some Lebesgue space, we look for weighted
spaces where boundedness (compact ness) holds. We develop the ideas
and the techniques for the derivation of appropriate conditions, in
terms of weights, which are equivalent to bounded ness
(compactness)."
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