Littlewood-Paley Analysis on Non Homogeneous Spaces

Part of the Lecture Notes in Mathematics book series (LNM, volume 1966)

It is well know that the doubling property of the underlying measure is a basic hypothesis in the classical Calderón-Zygmund theory. A measure μ on ℝn is said to be doubling if there exists some constant C such that μ(B(x, 2r)) ≤ cμ (B(x, r)) for all x ϵ supp(μ),r > 0, where \(B\left( {x,r} \right) = \left\{ {y \in R^n :\left| {y - x} \right| < r} \right\}\). Recently it has been shown that many results of the classical Calderón-Zygmund theory also hold without assuming the doubling property. See [GM], [MMNO], [NTV1], [NTV2], [NTV3], [T1], [T2] and [T3] for more material.

Suppose that μ is a Radon measure on ℝn, which may be non-doubling and only satisfies the growth condition, namely there is a constant C > 0 such that for all x ϵ supp(μ) and r > 0,
$$\mu \left( {B\left( {x,r} \right)} \right) \le C_0 r^d $$
where 0 > d ≤ n.


Homogeneous Space Besov Space Radon Measure Singular Integral Operator Homogeneous Type 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Personalised recommendations