We study the differentiation of integrals of functions in the Besov spaces B p (Rn), Î± > 0, 1 â‰¤ p < âˆž, with respect to the basis of arbitrarily oriented rectangular parallelepipeds in Rn. We showâ€¦ (More)

Starting from a slight modification of the dyadic sets introduced by M. Christ in [A T(b) theorem with remarks on analytic capacity and the Cauchy integral, Colloq. Math. 60/61 (1990) 601â€“628] on aâ€¦ (More)

In this paper we give conditions for the L2-boundedness of singular integrals and the weak type (1,1) of approximate identities on spaces of homogeneous type. Our main tools are Cotlar's lemma and anâ€¦ (More)

We give a very simple proof of the caracterization of Lipschitz regularity of a function by the size of its Haar coefficients. It is well known that given a real function I periodic with period 27râ€¦ (More)

We give a detailed proof, in the case of one space dimension, of a pointwise upper estimate for the space gradient of a temperature. The operators involved are a one-sided Hardy-Littlewood maximal inâ€¦ (More)

Given a rotation invariant measure in Rn, we define the maximal operator over circular sectors. We prove that it is of strong type (p, p) for p > 1 and we give necessary and sufficient conditions onâ€¦ (More)