Displaying similar documents to “Poisson-like kernels in tube domains over light-cones”

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...