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Averages over homogeneous hypersurfaces in R3.

Alex Iosevich (1996)

Forum mathematicum

Averages over hypersurfaces. II.

E.M. Stein, C.D. Sogge (1986)

Inventiones mathematicae

$B V$ 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:...