Maximal bilinear Calderón--Zygmund operators of type $\omega(t)$ on non-homogeneous space

Bilinear Calderón-Zygmund operators

This chapter is based on the presentation “Generalized bilinear CalderónZygmund operators and applications” delivered by the author during the 2008 February Fourier Talks at the Norbert Wiener Center for Harmonic Analysis and Applications, Department of Mathematics, University of Maryland, College Park, on February 21st. In turn, that presentation was based on material from the article “Weighte...

Weighted norm inequalities for Toeplitz type operators associated to generalized Calderón–Zygmund operators

Let [Formula: see text] be a generalized Calderón-Zygmund operator or [Formula: see text] ( the identity operator), let [Formula: see text] and [Formula: see text] be the linear operators, and let [Formula: see text]. Denote the Toeplitz type operator by [Formula: see text]where [Formula: see text] and [Formula: see text] is fractional integral operator. In this paper, we establish the sharp ma...

Bilinear Operators on Homogeneous Groups

Let Hp denote the Lebesgue space Lp for p > 1 and the Hardy space Hp for p ≤ 1. For 0 < p, q, r < ∞, we study Hp × Hq → Hr mapping properties of bilinear operators given by finite sums of products of Calderón–Zygmund operators on stratified homogeneous Lie groups. When r ≤ 1, we show that such mapping properties hold when a number of moments of the operator vanish. This hypothesis is natural an...

Fe b 20 00 BMO , H 1 , AND CALDERÓN - ZYGMUND OPERATORS FOR NON DOUBLING MEASURES

Given a Radon measure μ on R, which may be non doubling, we introduce a space of type BMO with respect to this measure. It is shown that many properties which hold for the classical space BMO(μ) when μ is a doubling measure remain valid for the space of type BMO introduced in this paper, without assuming μ doubling. For instance, Calderón-Zygmund operators which are bounded on L(μ) are also bou...

Volterra-Type Operators on Zygmund Spaces