O ct 2 00 8 WEIGHTED NORM INEQUALITIES , OFF - DIAGONAL ESTIMATES AND ELLIPTIC OPERATORS PASCAL
نویسنده
چکیده
We give an overview of the generalized Calderón-Zygmund theory for “non-integral” singular operators, that is, operators without kernels bounds but appropriate off-diagonal estimates. This theory is powerful enough to obtain weighted estimates for such operators and their commutators with BMO functions. L − L off-diagonal estimates when p ≤ q play an important role and we present them. They are particularly well suited to the semigroups generated by second order elliptic operators and the range of exponents (p, q) rules the L theory for many operators constructed from the semigroup and its gradient. Such applications are summarized.
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We prove weighted norm inequalities for fractional powers of elliptic operators together with their commutators with BMO functions, encompassing what is known for the classical Riesz potentials and elliptic operators with Gaussian domination by the classical heat operator. The method relies upon a good-λ method that does not use any size or smoothness estimates for the kernels.
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تاریخ انتشار 2008