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Lipschitz spaces and Calderón-Zygmund operators associated to non-doubling measures.

José García-Cuerva, A. Eduardo Gatto (2005)

Publicacions Matemàtiques

In the setting of a metric measure space (X, d, μ) with an n-dimensional Radon measure μ, we give a necessary and sufficient condition for the boundedness of Calderón-Zygmund operators associated to the measure μ on Lipschitz spaces on the support of μ. Also, for the Euclidean space Rd with an arbitrary Radon measure μ, we give several characterizations of Lipschitz spaces on the support of μ, Lip(α,μ), in terms of mean oscillations involving μ. This allows us to view the "regular" BMO space of...

Littlewood-Paley decompositions on manifolds with ends

Jean-Marc Bouclet (2010)

Bulletin de la Société Mathématique de France

For certain non compact Riemannian manifolds with ends which may or may not satisfy the doubling condition on the volume of geodesic balls, we obtain Littlewood-Paley type estimates on (weighted) L p spaces, using the usual square function defined by a dyadic partition.

Littlewood-Paley g-functions with rough kernels on homogeneous groups

Yong Ding, Xinfeng Wu (2009)

Studia Mathematica

Let 𝔾 be a homogeneousgroup on ℝⁿ whose multiplication and inverse operations are polynomial maps. In 1999, T. Tao proved that the singular integral operator with Llog⁺L function kernel on ≫ is both of type (p,p) and of weak type (1,1). In this paper, the same results are proved for the Littlewood-Paley g-functions on 𝔾

LP → LQ - Estimates for the Fractional Acoustic Potentials and some Related Operators

Karapetyants, Alexey, Karasev, Denis, Nogin, Vladimir (2005)

Fractional Calculus and Applied Analysis

Mathematics Subject Classification: 47B38, 31B10, 42B20, 42B15.We obtain the Lp → Lq - estimates for the fractional acoustic potentials in R^n, which are known to be negative powers of the Helmholtz operator, and some related operators. Some applications of these estimates are also given.* This paper has been supported by Russian Fond of Fundamental Investigations under Grant No. 40–01–008632 a.

Majoration de la transformée de Fourier de certaines mesures

Noël Lohoué, Jacques Peyrière (1983)

Annales de l'institut Fourier

Soit p une fonction polynôme de R m dans R . On considère la mesure μ p sur le graphe de p dont la projection sur R m est la mesure de Lebesgue. On étudie ici le comportement de la transformée de Fourier μ ^ p ( u , v ) lorsque v approche de 0 (de telles distributions apparaissent comme caractères de représentations de groupes de Lie nilpotents). On étend des résultats de L. Corwin et F.P. Greenleaf (Comm. on Pure and Applied Math., 31 (1975), 681–705) au cas où le gradient de la partie de p homogène de plus haut degré...

Marcinkiewicz integrals on product spaces

H. Al-Qassem, A. Al-Salman, L. C. Cheng, Y. Pan (2005)

Studia Mathematica

We prove the L p boundedness of the Marcinkiewicz integral operators μ Ω on ℝ n ₁ × ⋯ × ℝ n k under the condition that Ω ∈ L ( l o g L ) k / 2 ( n ₁ - 1 × ⋯ × n k - 1 ) . The exponent k/2 is the best possible. This answers an open question posed by Y. Ding.

Maximal inequalities and Riesz transform estimates on L p spaces for Schrödinger operators with nonnegative potentials

Pascal Auscher, Besma Ben Ali (2007)

Annales de l’institut Fourier

We show various L p estimates for Schrödinger operators - Δ + V on ℝ n and their square roots. We assume reverse Hölder estimates on the potential, and improve some results of Shen. Our main tools are improved Fefferman-Phong inequalities and reverse Hölder estimates for weak solutions of - Δ + V and their gradients.

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