Weighted norm inequalities, off-diagonal estimates and elliptic operators. Part II: Off-diagonal estimates on spaces of homogeneous typeReport as inadecuate




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1 LM-Orsay - Laboratoire de Mathématiques d-Orsay 2 IMFF - Instituto de Matematicas y Fisica Fundamental

Abstract : This is the second part of a series of four articles on weighted norm inequalities, off-diagonal estimates and elliptic operators. We consider a substitute to the notion of pointwise bounds for kernels of operators which usually is a measure of decay. This substitute is that of off-diagonal estimates expressed in terms of local and scale invariant $L^p-L^q$ estimates. We propose a definition in spaces of homogeneous type that is stable under composition. It is particularly well suited to semigroups. We study the case of semigroups generated by elliptic operators.

Keywords : Spaces of homogeneous type off-diagonal estimates Muckenhoupt weights semigroups elliptic operators





Author: Pascal Auscher - José Maria Martell -

Source: https://hal.archives-ouvertes.fr/



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