EUDML

We use the Calderón Maximal Function to prove the Kato-Ponce Product Rule Estimate and the Christ-Weinstein Chain Rule Estimate for the Hajłasz gradient on doubling measure metric spaces.

Weighted inequalities for commutators of fractional and singular integrals.

Carlos Segovia; José L. Torrea — 1991

Publicacions Matemàtiques

Equivalence of norms in one-sided Hp spaces.

Liliana de Rosa; Carlos Segovia — 2002

Collectanea Mathematica

One-sided versions of maximal functions for suitable defined distributions are considered. Weighted norm equivalences of these maximal functions for weights in the Sawyer's Aq+ classes are obtained.

On fractional differentiation and integration on spaces of homogeneous type.

A. Eduardo Gatto; Carlos Segovia; Stephen Vági — 1996

Revista Matemática Iberoamericana

In this paper we define derivatives of fractional order on spaces of homogeneous type by generalizing a classical formula for the fractional powers of the Laplacean [S1], [S2], [SZ] and introducing suitable quasidistances related to an approximation of the identity. We define integration of fractional order as in [GV] but using quasidistances related to the approximation of the identity mentioned before. We show that these operators act on Lipschitz spaces as in the classical cases....

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On the area function of Lusin

Weighted norm inequalities relating the $g *_{λ}$ and the area functions

Weighted norm inequalities for parabolic fractional integrals

Singular integrals on generalized Lipschitz and Hardy spaces

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

One-Sided Littlewood-Paley Theory.

Convergence of truncated singular integrals with two weights

Product rule and chain rule estimates for the Hajłasz gradient on doubling metric measure spaces

Weighted inequalities for commutators of fractional and singular integrals.

Equivalence of norms in one-sided Hp spaces.

On fractional differentiation and integration on spaces of homogeneous type.