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$B V$ spaces and rectifiability for Carnot-Carathéodory metrics: an introduction

Franchi, Bruno (2003)

Nonlinear Analysis, Function Spaces and Applications

This paper is meant as a (short and partial) introduction to the study of the geometry of Carnot groups and, more generally, of Carnot-Carathéodory spaces associated with a family of Lipschitz continuous vector fields. My personal interest in this field goes back to a series of joint papers with E. Lanconelli, where this notion was exploited for the study of pointwise regularity of weak solutions to degenerate elliptic partial differential equations. As stated in the title, here we are mainly concerned...

Balls and Quasi-Metrics: A Space of Homogenous Type Modeling the Real Analysis Related to the Monge-Ampère Equation.

H. Aimar, L. Forzani, R. Toledano (1998)

The journal of Fourier analysis and applications [[Elektronische Ressource]]

Behaviour of $L^{r}$ -Dini singular integrals in weighted $L^{1}$ spaces

Osvaldo Capri, Carlos Segovia (1989)

Studia Mathematica

Besicovitch Type Maximal Operators and Applications to Fourier Analysis.

J. Bourgain (1991)

Geometric and functional analysis

Besov and Triebel-Lizorkin spaces related to singular integrals with flag kernels.

Dachun Yang (2009)

Revista Matemática Complutense

Best constants and asymptotics of Marcinkiewicz-Zygmund inequalities

Andreas Defant, Marius Junge (1997)

Studia Mathematica

We determine the set of all triples 1 ≤ p,q,r ≤ ∞ for which the so-called Marcinkiewicz-Zygmund inequality is satisfied: There exists a constant c≥ 0 such that for each bounded linear operator $T : L_{q} (μ) \to L_{p} (ν)$ , each n ∈ ℕ and functions $f_{1}, . . ., f_{n} \in L_{q} (μ)$ , $(ʃ (\sum_{k = 1}^{n} | T f_{k} |^{r})^{p / r} {d ν)}^{1 / p} \leq c ∥ T ∥ (ʃ (\sum_{k = 1}^{n} | f_{k} |^{r} {)^{q / r} d μ)}^{1 / q}$ . This type of inequality includes as special cases well-known inequalities of Paley, Marcinkiewicz, Zygmund, Grothendieck, and Kwapień. If such a Marcinkiewicz-Zygmund inequality holds for a given triple (p,q,r), then we calculate the best constant c ≥ 0 (with the only exception:...

BIlinear Operators with Non-Smooth Symbol, I.

John E. Gilbert, Andrea R. Nahmod (2001)

The journal of Fourier analysis and applications [[Elektronische Ressource]]

BMO-Boundedness of Lusin's Area Function.

Milos Arsenovic, Miroljub Jevtic (1998)

Monatshefte für Mathematik

Boundary estimates for derivatives of harmonic functions

Frank Beatrous (1991)

Studia Mathematica

Boundedness for commutators of Littlewood-Paley operators on some Hardy spaces.

Liu, Lanzhe (2003)

Lobachevskii Journal of Mathematics

Boundedness for multilinear commutator of integral operator on Hardy and Herz-Hardy spaces.

Sheng, Ren, Liu, Lanzhe (2009)

Acta Universitatis Apulensis. Mathematics - Informatics

Boundedness for multilinear commutator of Littlewood--Paley operator on Hardy and Herz--Hardy spaces.

Wu, Changhong, Liu, Lanzhe (2009)

Acta Universitatis Apulensis. Mathematics - Informatics

Boundedness for multilinear commutator of Littlewood-Paley operator on Hardy and Herz-Hardy spaces.

Zeng, Jiasheng (2010)

Acta Universitatis Apulensis. Mathematics - Informatics

Boundedness for multilinear commutator of Littlewood-Paley operator on Hardy and Herz-Hardy spaces.

Wu, Changhong, Liu, Lanzhe (2006)

Lobachevskii Journal of Mathematics

Boundedness for multilinear Littlewood-Paley operators on Hardy and Herz-Hardy spaces.

Lanzhe Liu (2004)

Extracta Mathematicae

Boundedness for multilinear operators of multiplier operators on Triebel-Lizorkin and Lebesgue spaces.

Zhou, Xiaosha, Liu, Lanzhe (2009)

Acta Universitatis Apulensis. Mathematics - Informatics

Boundedness for multilinear singular integral operators on Morrey spaces.

Liu, Lanzhe (2010)

Bulletin of the Malaysian Mathematical Sciences Society. Second Series

Boundedness of classical operators on classical Lorentz spaces

E. Sawyer (1990)

Studia Mathematica

Boundedness of commutators of singular and potential operators in generalized grand Morrey spaces and some applications

Vakhtang Kokilashvili, Alexander Meskhi, Humberto Rafeiro (2013)

Studia Mathematica

In the setting of spaces of homogeneous type, it is shown that the commutator of Calderón-Zygmund type operators as well as the commutator of a potential operator with a BMO function are bounded in a generalized grand Morrey space. Interior estimates for solutions of elliptic equations are also given in the framework of generalized grand Morrey spaces.

Boundedness of fractional maximal operators between classical and weak-type Lorentz spaces [Book]

David E. Edmunds, Bohumír Opic (2002)

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