Let be a nonnegative Radon measure on which only satisfies for all , , with some fixed constants and In this paper, a new characterization for the space of Tolsa in terms of the John-Strömberg sharp maximal function is established.
Given a doubling measure μ on Rd, it is a classical result of harmonic analysis that Calderón-Zygmund operators which are bounded in L2(μ) are also of weak type (1,1). Recently it has been shown that the same result holds if one substitutes the doubling condition on μ by a mild growth condition on μ. In this paper another proof of this result is given. The proof is very close in spirit to the classical argument for doubling measures and it is based on a new Calderón-Zygmund decomposition adapted...
For a locally compact group G and p ∈ (1,∞), we define and study the Beurling-Figà-Talamanca-Herz algebras . For p = 2 and abelian G, these are precisely the Beurling algebras on the dual group Ĝ. For p = 2 and compact G, our approach subsumes an earlier one by H. H. Lee and E. Samei. The key to our approach is not to define Beurling algebras through weights, i.e., possibly unbounded continuous functions, but rather through their inverses, which are bounded continuous functions. We prove that...
We wish to acknowledge and correct an error in a proof in our paper On the product theory of singular integrals, which appeared in Revista Matemática Iberoamericana, volume 20, number 2, 2004, pages 531-561.
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
AMS Subj. Classification: MSC2010: 42C10, 43A50, 43A75We perform analysis of certain aspects of approximation in multiplicative systems that appear as duals of ultrametric structures, e.g. in cases of local fields, totally disconnected Abelian groups satisfying the second axiom of countability or more general ultrametric spaces that do not necessarily possess a group structure. Using the fact that the unit sphere of a local field is a Vilenkin group, we introduce a new concept of differentiation in...