In this note, by means of a kernel function induced continuous f on the unit circle, we show that corresponding integral operator Banach space AP is bounded or compact precisely when belongs to big Zygmund class ?* little ?*, where consists all holomorphic functions ? ?C\S1 with finite norm. This generalizes result in Hu, Song, Wei and Shen (2013) [5] meanwhile may be considered as infinitesima...

Abstract Let be an RD‐space, namely, a space of homogeneous type in the sense Coifman and Weiss with Borel measure μ satisfying reverse doubling condition on . Based this space, authors define multilinear strongly singular Calderón–Zygmund operator whose kernel does not need any size has more singularities near diagonal than that standard operator. For such operator, we establish its boundednes...

for all test functions f , where y′ = y/|y| ∈ Sn−1. We denote SIΩ,h( f ) by SIΩ( f ) if h= 1. The operator SIΩ was first studied by Calderón and Zygmund in their well-known papers (see [1, 2]). They proved that SIΩ is Lp(Rn) bounded, 1 < p < ∞, provided that Ω ∈ LLog+L(Sn−1) satisfying (1.1). They also showed that the space LLog+L(Sn−1) cannot be replaced by any Orlicz space Lφ(Sn−1) with a mon...

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...

1130 NOTICES OF THE AMS VOLUME 45, NUMBER 9 T he subject matter of this essay is Alberto Calderón’s pivotal role in the creation of the modern theory of singular integrals. In that great enterprise Calderón had the good fortune of working with Antoni Zygmund, who was at first his teacher and mentor and later his collaborator. For that reason any account of that theory has to be in part the stor...

Abstract. Given a doubling measure μ on R, it is a classical result of harmonic analysis that Calderón-Zygmund operators which are bounded in L(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...

We prove a Calderón-Zygmund type estimate which can be applied to sharpen known regularity results on spherical means, Fourier integral operators and generalized Radon transforms.

In this paper, we establish the boundedness of commutators generated by weighted Lipschitz functions and Calderón-Zygmund singular integral operators on weighted Herz spaces.

Abstract We prove weighted boundedness of Calderón–Zygmund and maximal singular operators in generalized Morrey spaces on quasi-metric measure spaces, general non-homogeneous, only under the growth condition measure, for a certain class weights. Weights characteristic are independent each other. Weighted operator is also proved case when lower upper Ahlfors exponents coincide with Our approach ...