Mathematics – Classical Analysis and ODEs
Scientific paper
2010-03-15
Mathematics
Classical Analysis and ODEs
Scientific paper
We introduce two new concepts, local homogeneity and local L^q-spectrum, both of which are tools that can be used in studying the local structure of measures. The main emphasis is given to the study of local dimensions of measures in doubling metric spaces. As an application, we reach a new level of generality and obtain new estimates for conical densities, in multifractal analysis, and on the dimension of porous measures.
Kaenmaki Antti
Rajala Tapio
Suomala Ville
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