Smooth and nonsmooth Calderon-Zygmund type decompositions for Morrey spaces

摘要

It is shown that it is possible to construct an analogue of the Colderon-Zygmund decomposition for the Morrey spaces Mor(lambda) for the entire interval lambda is an element of (0, 1]. Moreover, for lambda is an element of (1 - n/1], it is possible to contruct a smooth analogue of the Calder&-Zygmund decomposition. The reason why we do not have any smooth analogues for the entire interval lambda is an element of (0, 1] is related to the following interesting property of tubes in the Whitney decomposition lemma: The sum of fhe volumes of Whitney cubes to the power lambda is equal to infinity for lambda is an element of (0, 1 - n/1].