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Displaying similar documents to “On integral operators with operator-valued kernels.”

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...

Boundedness of some sublinear operators and commutators on Morrey-Herz spaces with variable exponents

Yan Lu, Yue Ping Zhu (2014)

Czechoslovak Mathematical Journal

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We introduce a new type of variable exponent function spaces M K ˙ q , p ( · ) α ( · ) , λ ( ℝ n ) of Morrey-Herz type where the two main indices are variable exponents, and give some propositions of the introduced spaces. Under the assumption that the exponents α and p are subject to the log-decay continuity both at the origin and at infinity, we prove the boundedness of a wide class of sublinear operators satisfying a proper size condition which include maximal, potential and Calderón-Zygmund operators and their commutators...