About: Singular integral operators of convolution type

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In mathematics, singular integral operators of convolution type are the singular integral operators that arise on Rn and Tn through convolution by distributions; equivalently they are the singular integral operators that commute with translations. The classical examples in harmonic analysis are the harmonic conjugation operator on the circle, the Hilbert transform on the circle and the real line, the Beurling transform in the complex plane and the Riesz transforms in Euclidean space. The continuity of these operators on L2 is evident because the Fourier transform converts them into multiplication operators. Continuity on Lp spaces was first established by Marcel Riesz. The classical techniques include the use of Poisson integrals, interpolation theory and the Hardy–Littlewood maximal funct

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rdfs:label	Singular integral operators of convolution type (en)
rdfs:comment	In mathematics, singular integral operators of convolution type are the singular integral operators that arise on Rn and Tn through convolution by distributions; equivalently they are the singular integral operators that commute with translations. The classical examples in harmonic analysis are the harmonic conjugation operator on the circle, the Hilbert transform on the circle and the real line, the Beurling transform in the complex plane and the Riesz transforms in Euclidean space. The continuity of these operators on L2 is evident because the Fourier transform converts them into multiplication operators. Continuity on Lp spaces was first established by Marcel Riesz. The classical techniques include the use of Poisson integrals, interpolation theory and the Hardy–Littlewood maximal funct (en)
rdfs:seeAlso	Beltrami equation Multiplier (Fourier analysis) Fatou's theorem Hardy–Littlewood maximal function Harmonic conjugate Hilbert transform Rising sun lemma
dcterms:subject	Singular integrals Operator theory Harmonic analysis
Wikipage page ID	36278557 (xsd:integer)
Wikipage revision ID	1119761501 (xsd:integer)
Link from a Wikipage to another Wikipage	Hardy-Littlewood maximal function Singular integrals Riesz transform Riesz–Thorin theorem Dominated convergence theorem Interpolation theory Marcinkiewicz interpolation theorem Riesz–Thorin interpolation theorem Operator theory Harmonic analysis Mathematics Operator norm G. H. Hardy Antoni Zygmund Lennart Carleson Hardy space Hardy–Littlewood maximal function Harmonic analysis Harmonic conjugate Pergamon Press Cauchy's integral formula Cauchy principal value Lebesgue differentiation theorem Lebesgue point Alberto Calderón Dual space Fourier transform Carleson measure Hilbert–Schmidt operator Hilbert transform Academic Press Distribution (mathematics) Dover Publications Marcel Riesz Paley-Wiener theorem Schwartz function Hölder's inequality Indicator function Rising sun lemma Strong operator topology Poisson kernel Lusin's conjecture Unit disk Beurling transform Fourier inversion formula Fourier multiplier Poisson integral Chebychev's inequality Principle of the argument Singular integral operator Singular integral operators F. Riesz
Link from a Wikipage to an external page	https://archive.org/details/introductiontofo0000stei http://www.ams.org/journals/bull/1966-72-03/S0002-9904-1966-11492-1/home.html%7Cdoi=10.1090/s0002-9904-1966-11492-1%7Cdoi-access=free
sameAs	Singular integral operators of convolution type Singular integral operators of convolution type Singular integral operators of convolution type Singular integral operators of convolution type
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has abstract	In mathematics, singular integral operators of convolution type are the singular integral operators that arise on Rn and Tn through convolution by distributions; equivalently they are the singular integral operators that commute with translations. The classical examples in harmonic analysis are the harmonic conjugation operator on the circle, the Hilbert transform on the circle and the real line, the Beurling transform in the complex plane and the Riesz transforms in Euclidean space. The continuity of these operators on L2 is evident because the Fourier transform converts them into multiplication operators. Continuity on Lp spaces was first established by Marcel Riesz. The classical techniques include the use of Poisson integrals, interpolation theory and the Hardy–Littlewood maximal function. For more general operators, fundamental new techniques, introduced by Alberto Calderón and Antoni Zygmund in 1952, were developed by a number of authors to give general criteria for continuity on Lp spaces. This article explains the theory for the classical operators and sketches the subsequent general theory. (en)
gold:hypernym	Operators
prov:wasDerivedFrom	wikipedia-en:Singular_integral_operators_of_convolution_type?oldid=1119761501&ns=0
page length (characters) of wiki page	70770 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Singular_integral_operators_of_convolution_type
is Link from a Wikipage to another Wikipage of	Calderón–Zygmund lemma

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