Marcinkiewicz-Zygmund Inequalities involving the zeros {xkn} of Jacobi polynomials for the weight wα,β can take the form

uniformly in x as h—»0, we shall say briefly that/ belongs to Lip a. Following 4](1)) we shall say that/ belongs to a) uniformly as *—>0. a notation already used (see Zygmund lipa, 0<a<l, if \f(x+h)-f(x)\=o(\h It is a classical result of Lebesgue (see Zygmund [5, p. 61 ] ; hereafter this book will be denoted by T.S.) that if / belongs to Lip a and if sn denotes the nth partial sum of the Fourie...

Some recent results for bilinear or multilinear singular integrals operators are presented. The focus is on some of the results that can be viewed as natural counterparts of classical theorems in Calderón-Zygmund theory, adding to the already existing extensive literature in the subject. In particular, two different classes of operators that can be seen as bilinear counterparts of linear Calder...

Abstract. As a step in developing a non-commutative Calderón–Zygmund theory, J. Parcet (J. Funct. Anal., 2009) established a new pseudo-localisation principle for classical singular integrals, showing that Tf has small L norm outside a set which only depends on f ∈ L but not on the arbitrary normalised Calderón–Zygmund operator T . Parcet also asked if a similar result holds true in L for p ∈ (...

For n + 1 = 2, these results had been established earlier by Plessner (1923) and by Marcinkiewicz and Zygmund (1938), who exploited the connection with holomorphic functions and mappings, including the conformal invariance of ∫ |f ′|2 for holomorphic f , and properties of conformal mappings of domains bounded by rectifiable curves. Concerning his motivation, Calderón discloses only that he aims...

In this work, we give new sufficient conditions for Littlewood-Paley-Stein square function and necessary and sufficient conditions for a Calderón-Zygmund operator to be bounded on Hardy spaces H p with indices smaller than 1. New Carleson measure type conditions are defined for Littlewood-Paley-Stein operators, and the authors show that they are sufficient for the associated square function to ...

The multilinear Calderón–Zygmund theory is developed in the setting of RD-spaces, namely, spaces of homogeneous type equipped with measures satisfying a reverse doubling condition. The multiple-weight multilinear Calderón–Zygmund theory in this context is also developed in this work. The bilinear T1-theorems for Besov and Triebel–Lizorkin spaces in the full range of exponents are among the main...

we investigate compact composition operators on ceratin lipschitzspaces of analytic functions on the closed unit disc of the plane.our approach also leads to some results about compositionoperators on zygmund type spaces.

This was first proved for Bernoulli random variables by Khintchine. Salem and Zygmund [SZ2] considered the case when the Xk are replaced by functions ak cosnkx on [−π, π] and gave an upper bound ( ≤ 1) result; this was extended to the full upper and lower bound by Erdös and Gál [EG]. Takahashi [T1] extends the result of Salem and Zygmund: Consider a real measurable function f satisfying f(x + 1...