Abstract
In this paper, we obtain the weighted endpoint estimates for the commutators of the singular integral operators with the BMO functions and the associated maximal operators on Orlicz-Morrey Spaces. We also get the similar results for the commutators of the fractional integral operators with the BMO functions and the associated maximal operators.
Highlights
Introduction and Main ResultsThe Morrey spaces were introduced by Morrey in [1] to investigate the local behavior of solutions to second-order elliptic partial differential equations
Chiarenza and Frasca [2] showed the boundedness of the Hardy-Littlewood maximal operator, singular integral operators, and the fractional integral operators on the Morrey spaces
0 < α < n, for an appropriate function f on Rn, the fractional integral operator of order α is defined by f (y)
Summary
The Morrey spaces were introduced by Morrey in [1] to investigate the local behavior of solutions to second-order elliptic partial differential equations. We obtain the weighted endpoint estimates for the commutators of the singular integral operators with BMO functions and associated maximal operators. We obtain the similar results for the commutators of the fractional integral operators with BMO functions and associated maximal operators. For the singular integral operator T and b ∈ BMO, the commutator [b, T] is defined by [b, T] f (x) = ∫ (b (x) − b (y)) K (x − y) f (y) dy. 0 < α < n, for an appropriate function f on Rn, the fractional integral operator (or the Riesz potential) of order α is defined by f (y). Let T be any singular integral operator, w ∈ A1, Φ(t) = t log(e + t), and b ∈ BMO.
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