For some pairs of weight functions u, v which satisfy the well-known Muckenhoupt conditions, we derive the boundedness of the maximal fractional operator Ms (0 ≤ s < n) from Lvp to Luq with q < p.
Let μ be a nonnegative Radon measure on which satisfies μ(B(x,r)) ≤ Crⁿ for any and r > 0 and some positive constants C and n ∈ (0,d]. In this paper, some weighted norm inequalities with weights of Muckenhoupt type are obtained for maximal singular integral operators with such a measure μ, via certain weighted estimates with weights of Muckenhoupt type involving the John-Strömberg maximal operator and the John-Strömberg sharp maximal operator, where ϱ,p ∈ [1,∞).
A weighted theory describing Morrey boundedness of fractional integral operators and fractional maximal operators is developed. A new class of weights adapted to Morrey spaces is proposed and a passage to the multilinear cases is covered.
In this paper we establish weighted norm inequalities for singular integral operators with kernel satisfying a variant of the classical Hörmander's condition.
Let X be a homogeneous space and let E be a UMD Banach space with a normalized unconditional basis . Given an operator T from to L¹(X), we consider the vector-valued extension T̃ of T given by . We prove a weighted integral inequality for the vector-valued extension of the Hardy-Littlewood maximal operator and a weighted Fefferman-Stein inequality between the vector-valued extensions of the Hardy-Littlewood and the sharp maximal operators, in the context of Orlicz spaces. We give sufficient...
Necessary and sufficient conditions are given for the Hardy-Littlewood maximal operator to be bounded on a weighted Orlicz space when the complementary Young function satisfies . Such a growth condition is shown to be necessary for any weighted integral inequality to occur. Weak-type conditions are also investigated.
We establish weighted sharp maximal function inequalities for a linear operator associated to a singular integral operator with non-smooth kernel. As an application, we obtain the boundedness of a commutator on weighted Lebesgue spaces.
We give a weighted version of the Sobolev-Lieb-Thirring inequality for suborthonormal functions. In the proof of our result we use phi-transform of Frazier-Jawerth.
Let be the Ariõ-Muckenhoupt weight class which controls the weighted -norm inequalities for the Hardy operator on non-increasing functions. We replace the constant p by a function p(x) and examine the associated -norm inequalities of the Hardy operator.
We consider the -weights and prove the weighted weak type (1,1) inequalities for certain oscillatory singular integrals.
We prove some weighted weak type (1,1) inequalities for certain singular integrals and Littlewood-Paley functions.