Displaying similar documents to “Higher integrability for maximal oscillatory Fourier integrals.”

On the boundedness of the maximal operator and singular integral operators in generalized Morrey spaces

Ali Akbulut, Vagif Guliyev, Rza Mustafayev (2012)

Mathematica Bohemica

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In the paper we find conditions on the pair ( ω 1 , ω 2 ) which ensure the boundedness of the maximal operator and the Calderón-Zygmund singular integral operators from one generalized Morrey space ℳ p , ω 1 to another ℳ p , ω 2 , 1 < p < ∞ , and from the space ℳ 1 , ω 1 to the weak space W ℳ 1 , ω 2 . As applications, we get some estimates for uniformly elliptic operators on generalized Morrey spaces.

Estimates for the commutator of bilinear Fourier multiplier

Guoen Hu, Wentan Yi (2013)

Czechoslovak Mathematical Journal

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Let b 1 , b 2 ∈ BMO ( ℝ n ) and T σ be a bilinear Fourier multiplier operator with associated multiplier σ satisfying the Sobolev regularity that sup κ ∈ ℤ ∥ σ κ ∥ W s 1 , s 2 ( ℝ 2 n ) < ∞ for some s 1 , s 2 ∈ ( n / 2 , n ] . In this paper, the behavior on L p 1 ( ℝ n ) × L p 2 ( ℝ n ) ( p 1 , p 2 ∈ ( 1 , ∞ ) ) , on H 1 ( ℝ n ) × L p 2 ( ℝ n ) ( p 2 ∈ [ 2 , ∞ ) ) , and on H 1 ( ℝ n ) × H 1 ( ℝ n ) , is considered for the commutator T σ , b → defined by T σ , b → ( f 1 , f 2 ) ( x ) = b 1 ( x ) T σ ( f 1 , f 2 ) ( x ) - T σ ( b 1 f 1 , f 2 ) ( x ) + b 2 ( x ) T σ ( f 1 , f 2 ) ( x ) - T σ ( f 1 , b 2 f 2 ) ( x ) . By kernel estimates of the bilinear Fourier multiplier operators and employing some techniques in the theory of bilinear singular integral operators, it is proved that these mapping properties are very similar to those...