CONTENTSIntroduction.......................................................................................................................................................... 5Chapter I. Some preliminary lemmas............................................................................................................ 8Chapter II. Weighted spaces of analytic functions.......................................................................... 13 1. Behaviour at the boundary..........................................................................................................................
I am going to discuss the work José Luis Rubio did on weighted norm inequalities. Most of it is in the book we wrote together on the subject [12].
The main purpose of this paper is to investigate the behavior of fractional integral operators associated to a measure on a metric space satisfying just a mild growth condition, namely that the measure of each ball is controlled by a fixed power of its radius. This allows, in particular, non-doubling measures. It turns out that this condition is enough to build up a theory that contains the classical results based upon the Lebesgue measure on Euclidean space and their known extensions for doubling...
In the setting of a metric measure space (X, d, μ) with an n-dimensional Radon measure μ, we give a necessary and sufficient condition for the boundedness of Calderón-Zygmund operators associated to the measure μ on Lipschitz spaces on the support of μ. Also, for the Euclidean space R with an arbitrary Radon measure μ, we give several characterizations of Lipschitz spaces on the support of μ, (α,μ), in terms of mean oscillations involving μ. This allows us to view the "regular" BMO space of X. Tolsa...
Recently, F. Nazarov, S. Treil and A. Volberg (and independently X. Tolsa) have extended the classical theory of Calderón-Zygmund operators to the context of a non-homogeneous space (X,d,μ) where, in particular, the measure μ may be non-doubling. In the present work we study weighted inequalities for these operators. Specifically, for 1 < p < ∞, we identify sufficient conditions for the weight on one side, which guarantee the existence of another weight in the other side, so that the...
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