{"title":"David E Edmunds","description":null,"products":[{"product_id":"bounded-and-compact-integral-operators-book-david-e-edmunds-9781402006197","title":"Bounded and Compact Integral Operators","description":"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).","brand":"WoB","offers":[{"title":"- \/ - \/ INTERNAL","offer_id":52414628561169,"sku":null,"price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ NEW \/ INGRAM","offer_id":52414629249297,"sku":"NLS9781402006197","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9781402006197.jpg?v=1785855576"},{"product_id":"hardy-operators-function-spaces-and-embeddings-book-david-e-edmunds-9783540219729","title":"Hardy Operators, Function Spaces and Embeddings","description":"Classical Sobolev spaces, based on Lebesgue spaces on an underlying domain with smooth boundary, are not only of considerable intrinsic interest but have for many years proved to be indispensible in the study of partial differential equations and variational problems.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52431866790161,"sku":"NLS9783540219729","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"US \/ NEW \/ INGRAM","offer_id":52761649447185,"sku":"NIN9783540219729","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783540219729.jpg?v=1791904683"},{"product_id":"bounded-and-compact-integral-operators-book-david-e-edmunds-9789048160181","title":"Bounded and Compact Integral Operators","description":"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.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52481673167121,"sku":"NLS9789048160181","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9789048160181.jpg?v=1791943939"},{"product_id":"representations-of-linear-operators-between-banach-spaces-book-david-e-edmunds-9783034806411","title":"Representations of Linear Operators Between Banach Spaces","description":"The book deals with the representation in series form of compact linear operators acting between Banach spaces, and provides an analogue of the classical Hilbert space results of this nature that have their roots in the work of D.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52660231930129,"sku":"NLS9783034806411","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"US \/ NEW \/ INGRAM","offer_id":53534439440657,"sku":"NIN9783034806411","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783034806411.jpg?v=1762264786"},{"product_id":"hardy-operators-function-spaces-and-embeddings-book-david-e-edmunds-9783642060274","title":"Hardy Operators, Function Spaces and Embeddings","description":"\u003cp\u003eClassical Sobolev spaces, based on Lebesgue spaces on an underlying domain with smooth boundary, are not only of considerable intrinsic interest but have for many years proved to be indispensible in the study of partial differential equations and variational problems. Many developments of the basic theory since its inception arise in response to concrete problems, for example, with the (ubiquitous) sets with fractal boundaries.\u003c\/p\u003e\n\u003cp\u003eThe theory will probably enjoy substantial further growth, but even now a connected account of the mature parts of it makes a useful addition to the literature. Accordingly, the main themes of this book are Banach spaces and spaces of Sobolev type based on them; integral operators of Hardy type on intervals and on trees; and the distribution of the approximation numbers (singular numbers in the Hilbert space case) of embeddings of Sobolev spaces based on generalised ridged domains.\u003c\/p\u003e\n\u003cp\u003eThis timely book will be of interest to all those concerned with the partial differential equations and their ramifications. A prerequisite for reading it is a good graduate course in real analysis.\u003c\/p\u003e","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52666390839569,"sku":"NLS9783642060274","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"US \/ NEW \/ INGRAM","offer_id":52761787334929,"sku":"NIN9783642060274","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783642060274.jpg?v=1762279837"}],"url":"https:\/\/www.worldofbooks.com\/collections\/author-books-by-david-e-edmunds.oembed","provider":"World of Books ","version":"1.0","type":"link"}