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

Pascal Auscher (1) , José Maria Martell (2)

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

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.

Mots clés: Spaces of homogeneous type; off-diagonal estimates; Muckenhoupt weights; semigroups; elliptic operators

Domaines: Analyse classique [math.CA]; Analyse fonctionnelle [math.FA]; Equations aux dérivées partielles [math.AP]

Pascal Auscher, José Maria Martell. Weighted norm inequalities, off-diagonal estimates and elliptic operators. Part II: Off-diagonal estimates on spaces of homogeneous type. Journal of Evolution Equations, 2007, 7 (2), pp.265-316. ⟨hal-00021877⟩