Calderón-Zygmund Operators, Pseudo-Differential Operators and the Cauchy Integral of Calderón

Journé, Jean-Lin

doi:10.1007/bfb0061458

Cited by 254 publications

(163 citation statements)

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“…The arguments for proving this result are in fact well known and can for example be found in the books of Journé [15] , García-Cuerva and Rubio de Francia [14]. The main difference is that assumption (IV) is valid only on a (later bounded) open set , which means that we have to localise the known results.…”

Section: Singular Integral Operatorsmentioning

confidence: 91%

“…For more informations on weighted spaces, we refer the interested reader to the books of Journé [15], Torchinsky [20], García-Cuerva and Rubio de Francia [14].…”

Section: ( )mentioning

confidence: 99%

“…Therefore we use a generalisation of a well known fact of Calderón and Scott [3,Proposition 4.7] to weighted spaces, which is in fact a more general version that the one used in the books of Journé [15], García-Cuerva and Rubio de Francia [14].…”

Section: Singular Integral Operatorsmentioning

confidence: 99%

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The divergence equation in weighted- and L p(·)-spaces

Huber

2009

Math. Z.

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We study the solvability of the divergence equation in weighted spaces and Lebesgue spaces with variable exponents, where the weights are so called Muckenhoupt weights. The question of constructing divergence free test functions, which can be used for problems arising in fluid dynamics, is also addressed. The approach is based on an explicit representation formula for solutions of the divergence equation due to Bogovskiȋ and the theory of singular integral operators. The developed methods are used to prove an existence result for fluids which satisfy a p(·)-growth condition.

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Section: Singular Integral Operatorsmentioning

confidence: 91%

“…For more informations on weighted spaces, we refer the interested reader to the books of Journé [15], Torchinsky [20], García-Cuerva and Rubio de Francia [14].…”

Section: ( )mentioning

confidence: 99%

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The divergence equation in weighted- and L p(·)-spaces

Huber

2009

Math. Z.

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“…The proof of this fact consists in adapting the scalar case to this vector valued case. For the scalar case see [8]. These equivalences have as a consequence that any of them is equivalent to the following statement: (iii) There exists a constant …”

Section: N We Use the Notations In (7) And (8)mentioning

confidence: 92%

Hermite Function Expansions Versus Hermite Polynomial Expansions

Abu-Falahah¹,

Torrea²

2006

Glasgow Math. J.

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Abstract. We consider expansions with respect to the multi-dimensional Hermite functions and to the multi-dimensional Hermite polynomials. They are respectively eigenfunctions of the Harmonic oscillator L = − + |x| 2 and of the OrnsteinUhlenbeck operator L = − + 2x · ∇. The corresponding heat semigroups and Riesz transforms are considered and results on both aspects (polynomials and functions) are obtained.2000 Mathematics Subject Classification. 42C10, 42B20, 42B25.

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“…We cite the articles in various Proceedings of the International Congress of Mathematics that were written by Calderón, Stein, C. Fefferman and G. David [4,26,17,13]. Other excellent sources are the book by Journé [22] and the book edited by Stein [27].…”

Section: The Tl Theorem a Calderón-zygmund Operator T Is Bounded On mentioning

confidence: 99%

Book Review: Real variable methods in harmonic analysis

Weiss¹

1989

Bull. Amer. Math. Soc.

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Calderón-Zygmund Operators, Pseudo-Differential Operators and the Cauchy Integral of Calderón

Cited by 254 publications

References 0 publications

The divergence equation in weighted- and L p(·)-spaces

The divergence equation in weighted- and L p(·)-spaces

Hermite Function Expansions Versus Hermite Polynomial Expansions

Book Review: Real variable methods in harmonic analysis

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