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

摘要

This is the second part of a series of four articles on weighted norminequalities, off-diagonal estimates and elliptic operators. We consider asubstitute to the notion of pointwise bounds for kernels of operators whichusually is a measure of decay. This substitute is that of off-diagonalestimates 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 undercomposition. It is particularly well suited to semigroups. We study the case ofsemigroups generated by elliptic operators.