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.
In this paper, the boundedness properties for some Toeplitz type operators associated to the Riesz potential and general integral operators from Lebesgue spaces to Orlicz spaces are proved. The general integral operators include singular integral operator with general kernel, Littlewood-Paley operator, Marcinkiewicz operator and Bochner-Riesz operator.
We prove a multi-parameter Hilbert-type integral inequality with a hybrid kernel. We describe the best constant in the inequality in terms of hypergeometric functions. Some equivalent forms of the inequalities are also studied. By specifying parameter values we obtain results proved by other authors as well as many new inequalities.
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