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

Pascal Auscher·José Maria Martell
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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.

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Pascal Auscher, José Maria Martell. 2006-03-28. Weighted norm inequalities, off-diagonal estimates and elliptic operators. Part II: Off-diagonal estimates on spaces of homogeneous type. https://doi.org/10.1007/s00028-007-0288-9

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