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 Lp − Lq 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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This work was partially supported by the European Union (IHP Network “Harmonic Analysis and Related Problems” 2002-2006, Contract HPRN-CT-2001-00273-HARP). The second author was also supported by MEC “Programa Ramón y Cajal, 2005” and by MEC Grant MTM2004-00678.
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Auscher, P., Martell, J.M. Weighted norm inequalities, off-diagonal estimates and elliptic operators Part II: Off-diagonal estimates on spaces of homogeneous type. J. evol. equ. 7, 265–316 (2007). https://doi.org/10.1007/s00028-007-0288-9
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DOI: https://doi.org/10.1007/s00028-007-0288-9