Displaying similar documents to “A new framework for generalized Besov-type and Triebel-Lizorkin-type spaces”

Boundedness of Hardy-Littlewood maximal operator in the framework of Lizorkin-Triebel spaces.

Soulaymane Korry (2002)

Revista Matemática Complutense

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We describe a class O of nonlinear operators which are bounded on the Lizorkin-Triebel spaces F (R), for 0 < s < 1 and 1 < p, q < ∞. As a corollary, we prove that the Hardy-Littlewood maximal operator is bounded on F (R), for 0 < s < 1 and 1 < p, q < ∞ ; this extends the result of Kinnunen (1997), valid for the Sobolev space H (R).

Multiplier operators on product spaces

Hung Viet Le (2002)

Studia Mathematica

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The author proves the boundedness for a class of multiplier operators on product spaces. This extends a result obtained by Lung-Kee Chen in 1994.

Fourier analysis in several parameters.

Robert Fefferman (1986)

Revista Matemática Iberoamericana

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Clearly, one of the most basic contributions to the fields of real variables, partial differential equations and Fourier analysis in recent times has been the celebrated theorem of Calderón and Zygmund on the boundedness of singular integrals on R [1].

A₁-regularity and boundedness of Calderón-Zygmund operators

Dmitry V. Rutsky (2014)

Studia Mathematica

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The Coifman-Fefferman inequality implies quite easily that a Calderón-Zygmund operator T acts boundedly in a Banach lattice X on ℝⁿ if the Hardy-Littlewood maximal operator M is bounded in both X and X'. We establish a converse result under the assumption that X has the Fatou property and X is p-convex and q-concave with some 1 < p, q < ∞: if a linear operator T is bounded in X and T is nondegenerate in a certain sense (for example, if T is a Riesz transform) then M is bounded...

Multilinear analysis on metric spaces

Loukas Grafakos, Liguang Liu, Diego Maldonado, Dachun Yang

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The multilinear Calderón-Zygmund theory is developed in the setting of RD-spaces which are spaces of homogeneous type equipped with measures satisfying a reverse doubling condition. The multiple-weight multilinear Calderón-Zygmund theory in this context is also developed in this work. The bilinear T1-theorems for Besov and Triebel-Lizorkin spaces in the full range of exponents are among the main results obtained. Multilinear vector-valued T1 type theorems on Lebesgue spaces, Besov spaces,...

Vector-valued wavelets and the Hardy space H¹(ℝⁿ,X)

Tuomas Hytönen (2006)

Studia Mathematica

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We prove an analogue of Y. Meyer's wavelet characterization of the Hardy space H¹(ℝⁿ) for the space H¹(ℝⁿ,X) of X-valued functions. Here X is a Banach space with the UMD property. The proof uses results of T. Figiel on generalized Calderón-Zygmund operators on Bochner spaces and some new local estimates.

Variants of the Calderón-Zygmund theory for L-spaces.

Anthony Carbery (1986)

Revista Matemática Iberoamericana

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The purposes of this paper may be described as follows: (i) to provide a useful substitute for the Cotlar-Stein lemma for Lp-spaces (the orthogonality conditions are replaced by certain fairly weak smoothness asumptions); (ii) to investigate the gap between the Hörmander multiplier theorem and the Littman-McCarthy-Rivière example - just how little regularity is really needed? (iii) to simplify and extend the work of Duoandikoetxea...