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By David E. Edmunds,V.M Kokilashvili,Alexander Meskhi

ISBN-10: 1402006195

ISBN-13: 9781402006197

ISBN-10: 9048160189

ISBN-13: 9789048160181

The monograph offers many of the authors' fresh and unique effects bearing on boundedness and compactness difficulties in Banach functionality areas either for classical operators and indispensable transforms outlined, often conversing, on nonhomogeneous areas. Itfocuses onintegral operators certainly coming up in boundary worth difficulties for PDE, the spectral conception of differential operators, continuum and quantum mechanics, stochastic strategies and so on. The booklet might be regarded as a scientific and specific research of a giant type of particular vital operators from the boundedness and compactness perspective. A attribute function of the monograph is that the majority of the statements proved right here have the shape of standards. those standards let us, for instance, togive var­ ious particular examples of pairs of weighted Banach functionality areas governing boundedness/compactness of a large type of essential operators. The ebook has major elements. the 1st half, which include Chapters 1-5, covers theinvestigation ofclassical operators: Hardy-type transforms, fractional integrals, potentials and maximal services. Our major target is to provide a whole description of these Banach functionality areas during which the above-mentioned operators act boundedly (com­ pactly). whilst a given operator isn't really bounded (compact), for instance in a few Lebesgue area, we glance for weighted areas the place boundedness (compact­ ness) holds. We enhance the guidelines and the strategies for the derivation of acceptable stipulations, by way of weights, that are such as bounded­ ness (compactness).

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Bounded and Compact Integral Operators (Mathematics and Its Applications) by David E. Edmunds,V.M Kokilashvili,Alexander Meskhi

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