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• W2555026510 abstract "As the development of singular integral operators [4, 18, 19], their commutators have been well studied. In [3, 16, 17], the authors proved that the commutators generated by the singular integral operators and BMO functions are bounded on p L ( p R ) for 1 p < < ∞ . Chanillo [2] proved a similar result when singular integral operators are replaced by the fractional integral operators. In [5], Janson proved the boundedness for the commutators generated by the singular integral operators and BMO functions from Lebesgue spaces to Orlicz spaces. Motivated by these papers, in this paper, we will introduce some Toeplitz type operators associated to certain fractional integral operators with general kernels [1, 8] and prove the boundedness properties of the Toeplitz type operators from Lebesgue spaces to Orlicz spaces. The fractional integral operators include singular integral operator with general kernel, Riesz potential operator with rough kernel, Littlewood-Paley operator and Marcinkiewicz operator. First, let us introduce some notations. Throughout this paper, Q will denote a cube of n R with sides parallel to the axes. For any locally integrable function f, the sharp function of f is defined by" @default.
• W2555026510 created "2016-11-30" @default.
• W2555026510 creator A5031522396 @default.
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• W2555026510 date "2015-01-01" @default.
• W2555026510 modified "2023-09-24" @default.
• W2555026510 title "BOUNDEDNESS OF TOEPLITZ TYPE OPERATOR RELATED TO GENERAL FRACTIONAL INTEGRAL OPERATORS ON ORLICZ SPACE" @default.
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