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1
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$L^{p}(ℝⁿ)$ boundedness for the commutator of a homogeneous singular integral operator

100%
Hu G.
Studia Mathematica
|
2003
|
tom 154
|
nr 1
13-27
EN
The commutator of a singular integral operator with homogeneous kernel Ω(x)/|x|ⁿ is studied, where Ω is homogeneous of degree zero and has mean value zero on the unit sphere. It is proved that $Ω ∈ L(log L)^{k+1}(S^{n-1})$ is a sufficient condition for the kth order commutator to be bounded on $L^{p}(ℝⁿ)$ for all 1 < p < ∞. The corresponding maximal operator is also considered.
2
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Weighted norm inequalities for maximal singular integrals with nondoubling measures

63%
Hu G., Yang D.
Studia Mathematica
|
2008
|
tom 187
|
nr 2
101-123
EN
Let μ be a nonnegative Radon measure on $ℝ^{d}$ which satisfies μ(B(x,r)) ≤ Crⁿ for any $x ∈ ℝ^{d}$ and r > 0 and some positive constants C and n ∈ (0,d]. In this paper, some weighted norm inequalities with $A_{p}^{ϱ}(μ)$ weights of Muckenhoupt type are obtained for maximal singular integral operators with such a measure μ, via certain weighted estimates with $A_{∞}^{ϱ}(μ)$ weights of Muckenhoupt type involving the John-Strömberg maximal operator and the John-Strömberg sharp maximal operator, where ϱ,p ∈ [1,∞).
3
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A variant sharp estimate for multilinear singular integral operators

63%
Hu G., Yang D.
Studia Mathematica
|
2000
|
tom 141
|
nr 1
25-22
EN
We establish a variant sharp estimate for multilinear singular integral operators. As applications, we obtain the weighted norm inequalities on general weights and certain $Llog^{+}L$ type estimates for these multilinear operators.
4
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$L^{p}(ℝⁿ)$ bounds for commutators of convolution operators

51%
Hu G., Sun Q., Wang X.
Colloquium Mathematicum
|
2002
|
tom 93
|
nr 1
11-20
EN
The $L^{p}(ℝⁿ)$ boundedness is established for commutators generated by BMO(ℝⁿ) functions and convolution operators whose kernels satisfy certain Fourier transform estimates. As an application, a new result about the $L^{p}(ℝⁿ)$ boundedness is obtained for commutators of homogeneous singular integral operators whose kernels satisfy the Grafakos-Stefanov condition.
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