Multilinear analysis on metric spaces

Loukas Grafakos; Liguang Liu; Diego Maldonado; Dachun Yang

Displaying similar documents to “Multilinear analysis on metric spaces”

Some new spaces of Besov and Triebel-Lizorkin type on homogeneous spaces

Yongsheng Han, Dachun Yang (2003)

Studia Mathematica

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New norms for some distributions on spaces of homogeneous type which include some fractals are introduced. Using inhomogeneous discrete Calderón reproducing formulae and the Plancherel-Pólya inequalities on spaces of homogeneous type, the authors prove that these norms give a new characterization for the Besov and Triebel-Lizorkin spaces with p, q > 1 and can be used to introduce new inhomogeneous Besov and Triebel-Lizorkin spaces with p, q ≤ 1 on spaces of homogeneous type. Moreover,...

On multilinear singular integrals of Calderón-Zygmund type.

Loukas Grafakos, Rodolfo H. Torres (2002)

Publicacions Matemàtiques

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A variety of results regarding multilinear singular Calderón-Zygmund integral operators is systematically presented. Several tools and techniques for the study of such operators are discussed. These include new multilinear endpoint weak type estimates, multilinear interpolation, appropriate discrete decompositions, a multilinear version of Schur's test, and a multilinear version of the T1 Theorem suitable for the study of multilinear pseudodifferential and translation invariant operators....

Tractable embeddings of Besov spaces into Zygmund spaces, II

Hans Triebel (2014)

Banach Center Publications

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The paper deals with dimension-controllable (tractable) embeddings of Besov spaces on n-dimensional cubes into Zygmund spaces.

Calderón-type reproducing formula and the Tb theorem.

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.

Calderón-Zygmund operators on product spaces.

Jean-Lin Journé (1985)

Revista Matemática Iberoamericana

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Tractable embeddings of Besov spaces into Zygmund spaces

Hans Triebel (2011)

Banach Center Publications

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The paper deals with dimension-controllable (tractable) embeddings of Besov spaces on n-dimensional cubes into Zygmund spaces. This can be expressed in terms of tractability envelopes.

Vector-valued Calderón-Zygmund theory and Carleson measures on spaces of homogeneous nature

Francisco Ruiz, José Torrea (1988)

Studia Mathematica

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Generalized homogeneous Besov spaces and their applications

Mejjaoli, Hatem (2012)

Serdica Mathematical Journal

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2010 Mathematics Subject Classification: Primary 35L05. Secondary 46E35, 35J25, 22E30. In this paper we define the homogeneous Besov spaces associated with the Dunkl operators on R^d, and we give a complete analysis on these spaces and same applications.

Molecules in coorbit spaces and boundedness of operators

Karlheinz Gröchenig, Mariusz Piotrowski (2009)

Studia Mathematica

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We study the notion of molecules in coorbit spaces. The main result states that if an operator, originally defined on an appropriate space of test functions, maps atoms to molecules, then it can be extended to a bounded operator on coorbit spaces. For time-frequency molecules we recover some boundedness results on modulation spaces, for time-scale molecules we obtain the boundedness on homogeneous Besov spaces.

Multilinear Calderón-Zygmund operators on weighted Hardy spaces

Wenjuan Li, Qingying Xue, Kôzô Yabuta (2010)

Studia Mathematica

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Grafakos-Kalton [Collect. Math. 52 (2001)] discussed the boundedness of multilinear Calderón-Zygmund operators on the product of Hardy spaces. Then Lerner et al. [Adv. Math. 220 (2009)] defined $A_{p ⃗}$ weights and built a theory of weights adapted to multilinear Calderón-Zygmund operators. In this paper, we combine the above results and obtain some estimates for multilinear Calderón-Zygmund operators on weighted Hardy spaces and also obtain a weighted multilinear version of an inequality for...

Hardy space estimates for multilinear operators (I).

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.

The boundedness of Calderón-Zygmund operators on the spaces F .

Michel Frazier, Rodolfo Torres, Guido Weiss (1988)

Revista Matemática Iberoamericana

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Calderón-Zygmund operators are generalizations of the singular integral operators introduced by Calderón and Zygmund in the fifties [CZ]. These singular integrals are principal value convolutions of the form Tf(x) = lím_ε→0 ∫_|x-y|>ε K(x-y) f(y) dy = p.v.K * f(x), where f belongs to some class of test functions.

Brézis-Gallouët-Wainger type inequality for Besov-Morrey spaces

Yoshihiro Sawano (2010)

Studia Mathematica

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The aim of the present paper is to obtain an inequality of Brézis-Gallouët-Wainger type for Besov-Morrey spaces. We investigate these spaces in a self-contained manner. Also, we verify that our result is sharp.

Equivalent norms in spaces of Besov-Triebel-Lizorkin type defined by pseudodifferential operators

H.-G. Leopold (1989)

Banach Center Publications

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Regularity properties of singular integral operators

Abdellah Youssfi (1996)

Studia Mathematica

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For s>0, we consider bounded linear operators from $D (ℝ^{n})$ into $D^{'} (ℝ^{n})$ whose kernels K satisfy the conditions $| \partial_{x}^{γ} K (x, y) | \leq C_{γ} {| x - y |}^{- n + s - | γ |}$ for x≠y, |γ|≤ [s]+1, $| \nabla_{y} \partial_{x}^{γ} K (x, y) | \leq C_{γ} {| x - y |}^{- n + s - | γ | - 1}$ for |γ|=[s], x≠y. We establish a new criterion for the boundedness of these operators from $L^{2} (ℝ^{n})$ into the homogeneous Sobolev space $Ḣ^{s} (ℝ^{n})$ . This is an extension of the well-known T(1) Theorem due to David and Journé. Our arguments make use of the function T(1) and the BMO-Sobolev space. We give some applications to the Besov and Triebel-Lizorkin spaces as well as some...

A new framework for generalized Besov-type and Triebel-Lizorkin-type spaces

Yiyu Liang, Dachun Yang, Wen Yuan, Yoshihiro Sawano, Tino Ullrich

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In this paper, the authors propose a new framework under which a theory of generalized Besov-type and Triebel-Lizorkin-type function spaces is developed. Many function spaces appearing in harmonic analysis fall under the scope of this new framework. The boundedness of the Hardy-Littlewood maximal operator or the related vector-valued maximal function on any of these function spaces is not required to construct these generalized scales of smoothness spaces. Instead, a key idea used is...

Convolution operators on Hardy spaces

Chin-Cheng Lin (1996)

Studia Mathematica

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We give sufficient conditions on the kernel K for the convolution operator Tf = K ∗ f to be bounded on Hardy spaces $H^{p} (G)$ , where G is a homogeneous group.

Vector valued inequalities for strongly singular Calderón-Zygmund operators.

Josefina Alvarez, Mario Milman (1986)

Revista Matemática Iberoamericana

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In this article we consider a theory of vector valued strongly singular operators. Our results include L^p, H^p and BMO continuity results. Moreover, as is well known, vector valued estimates are closely related to weighted norm inequalities. These results are developed in the first four sections of our paper. In section 5 we use our vector valued singular integrals to estimate the corresponding maximal operators. Finally in section 6 we discuss...