In this paper, we introduce a class of non-convolution-type Calderón-Zygmund operators, whose kernels are certain sums involving the products of the Daubechies wavelets and their convolutions. And we obtain the c...In this paper, we introduce a class of non-convolution-type Calderón-Zygmund operators, whose kernels are certain sums involving the products of the Daubechies wavelets and their convolutions. And we obtain the continuity on the Besov spaces B 0,q p (1 ≤ p, q ≤∞), which is mainly dependent on the properties of the Daubechies wavelets and Lemari's T1 theorem for Besov spaces.展开更多
Suppose μ is a Radon measure on R^d, which may be non doubling. The only condition assumed on μ is a growth condition, namely, there is a constant Co 〉 0 such that for all x ∈ supp（μ） and r 〉 0, μ（B（x, r）...Suppose μ is a Radon measure on R^d, which may be non doubling. The only condition assumed on μ is a growth condition, namely, there is a constant Co 〉 0 such that for all x ∈ supp（μ） and r 〉 0, μ（B（x, r）） ≤ Cor^n, where 0 〈 n ≤ d. We prove T1 theorem for non doubling measures with weak kernel conditions. Our approach yields new results for kernels satisfying weakened regularity conditions, while recovering previously known Tolsa＇s results. We also prove T1 theorem for Besov spaces on nonhomogeneous spaces with weak kernel conditions given in [7] .展开更多
This paper focuses on the study of the boundedness of convolution-type Calderón-Zygmund operators on some endpoint Triebel-Lizorkin spaces. Applying wavelets, molecular decomposition and interpolation theory, the...This paper focuses on the study of the boundedness of convolution-type Calderón-Zygmund operators on some endpoint Triebel-Lizorkin spaces. Applying wavelets, molecular decomposition and interpolation theory, the author establishes the boundedness on certain endpoint Triebel-Lizorkin spaces F˙10 ,q（2 q ≤ ∞） under a very weak pointwise regularity condition.展开更多
基金Supported by the Special Fund for Basic Scientific Research of Central Colleges, South-Central University for Nationalities(ZZQ10010)Supported by the Fund for the Doctoral Program of Higher Education(20090141120010)
文摘In this paper, we introduce a class of non-convolution-type Calderón-Zygmund operators, whose kernels are certain sums involving the products of the Daubechies wavelets and their convolutions. And we obtain the continuity on the Besov spaces B 0,q p (1 ≤ p, q ≤∞), which is mainly dependent on the properties of the Daubechies wavelets and Lemari's T1 theorem for Besov spaces.
基金The project was supported by the National Natural Science Fbundation of China(Grant No.10171111)the Foundation of Zhongshan University Advanced Research Center.
文摘Suppose μ is a Radon measure on R^d, which may be non doubling. The only condition assumed on μ is a growth condition, namely, there is a constant Co 〉 0 such that for all x ∈ supp（μ） and r 〉 0, μ（B（x, r）） ≤ Cor^n, where 0 〈 n ≤ d. We prove T1 theorem for non doubling measures with weak kernel conditions. Our approach yields new results for kernels satisfying weakened regularity conditions, while recovering previously known Tolsa＇s results. We also prove T1 theorem for Besov spaces on nonhomogeneous spaces with weak kernel conditions given in [7] .
基金Supported by the National Natural Science Foundation of China (Grant No. 10871209)Research Fund for the Doctoral Program of Higher Education (Grant No. 20090141120010)
文摘This paper focuses on the study of the boundedness of convolution-type Calderón-Zygmund operators on some endpoint Triebel-Lizorkin spaces. Applying wavelets, molecular decomposition and interpolation theory, the author establishes the boundedness on certain endpoint Triebel-Lizorkin spaces F˙10 ,q（2 q ≤ ∞） under a very weak pointwise regularity condition.
