This volume gives an account of the current state of weight theory for integral operators, such as maximal functions, Riesz potential, singular integrals and their generalization in Lorentz and Orlicz spaces. Starting with the crucial concept of a space of homogeneous type, it continues with general criteria for the boundedness of the integral operators considered, then address special settings and applications to classical operators in Euclidean spaces.
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Definition. A space of homogeneous type (SHT in the following) (X, d,) is a topological space endowed with a measure such that the space of compactly supported continuous functions is dense in L1(X,) and there exists a non-negative real-valued function d : X x X R1 satisfying (i) d(x,x) = 0 for all x X. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
transforms with positive kernel, reverse doubling condition, fractional maximal functions, maximal functions and singular integrals, two weight inequalities, modular inequalities, inequalities for singular integrals, modular inequality, maximal singular integrals, classical singular integrals, weight inequality, locally finite measure, sup ess, weighted inequalities, weak type, covering lemma, quasiconvex functions, positive decreasing functions, interpolation argument, disjoint balls, strong type Key Phrases - Capitalized Phrases (CAPs): (learn more)
Using Theorem, Applying Hölder, Applying Theorem New!
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Definition. A space of homogeneous type (SHT in the following) (X, d,) is a topological space endowed with a measure such that the space of compactly supported continuous functions is dense in L1(X,) and there exists a non-negative real-valued function d : X x X R1 satisfying (i) d(x,x) = 0 for all x X. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
transforms with positive kernel, reverse doubling condition, fractional maximal functions, maximal functions and singular integrals, two weight inequalities, modular inequalities, inequalities for singular integrals, modular inequality, maximal singular integrals, classical singular integrals, weight inequality, locally finite measure, sup ess, weighted inequalities, weak type, covering lemma, quasiconvex functions, positive decreasing functions, interpolation argument, disjoint balls, strong type Key Phrases - Capitalized Phrases (CAPs): (learn more)
Using Theorem, Applying Hölder, Applying Theorem New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 9
books:
See all 9 books this book cites
3
books
cite this book:
- Harmonic Analysis by Elias M. Stein in Back Matter
- Fourier Analysis on Local Fields (Mathematical Notes) by M. H. Taibleson in Back Matter
- Hardy Spaces on Homogeneous Groups. (MN-28): (Mathematical Notes) by Gerald B. Folland in Back Matter
- Weighted Inequalities and Degenerate Elliptic Partial Differential Equations (Lecture Notes in Mathematics; 1074) by Edward William Stredulinsky in Back Matter
- Weighted Hardy Spaces (Lecture Notes in Mathematics) by Jan-Olov Stromberg in Back Matter
See all 9 books this book cites
- Hypersingular Integrals and Their Applications (Analytical Methods and Special Functions) by Stefan Samko in Back Matter
- Factorization, Singular Operators and Related Problems by Stefan Samko on page 194
- Unilateral Contact Problems: Variational Methods and Existence Theorems (Chapman & Hall/CRC Pure and Applied Mathematics) by Christof Eck in Back Matter
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