A semilinear equation in
Philippe Benilan, Haim Brezis, Michael G. Crandall (1975)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Philippe Benilan, Haim Brezis, Michael G. Crandall (1975)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Robert Fefferman (1985)
Revista Matemática Iberoamericana
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Yong Sheng Han (1994)
Revista Matemática Iberoamericana
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In this paper we use the Calderón-Zygmund operator theory to prove a Calderón type reproducing formula associated with a para-accretive function. Using our Calderón-type reproducing formula we introduce a new class of the Besov and Triebel-Lizorkin spaces and prove a Tb theorem for these new spaces.
Yongsheng Han, Eric T. Sawyer (1990)
Revista Matemática Iberoamericana
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G. David, J.-L. Journé and S. Semmes have shown that if b and b are para-accretive functions on R, then the Tb theorem holds: A linear operator T with Calderón-Zygmund kernel is bounded on L if and only if Tb ∈ BMO, T*b ∈ BMO and MTM has the weak boundedness property. Conversely they showed that when b = b = b, para-accretivity of b is necessary for Tb Theorem to hold. In this paper we show that para-accretivity of both b and b is necessary for the Tb Theorem to hold in general. In addition,...
Steve Hofmann (1994)
Revista Matemática Iberoamericana
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We prove Lp (and weighted Lp) bounds for singular integrals of the form p.v. ∫Rn E (A(x) - A(y) / |x - y|) (Ω(x - y) / |x - y|n) f(y) dy, where E(t) = cos t if Ω is odd, and E(t) = sin t if Ω is even, and where ∇ A ∈ BMO. Even in the case that Ω is smooth, the theory of singular integrals with rough kernels plays a key role in the...
Josefina Alvarez (1998)
Collectanea Mathematica
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A. Lerner (2000)
Studia Mathematica
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We prove two pointwise estimates relating some classical maximal and singular integral operators. In particular, these estimates imply well-known rearrangement inequalities, and BLO-norm inequalities
Ronald R. Coifman, Loukas Grafakos (1992)
Revista Matemática Iberoamericana
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In this article we study bilinear operators given by inner products of finite vectors of Calderón-Zygmund operators. We find that necessary and sufficient condition for these operators to map products of Hardy spaces into Hardy spaces is to have a certain number of moments vanishing and under this assumption we prove a Hölder-type inequality in the H space context.
Norman G. Meyers (1963)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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