A NOTE ON SINGULAR INTEGRALS WITH DOMINATING MIXED SMOOTHNESS IN TRIEBEL-LIZORKIN SPACES

doi:10.1016/S0252-9602(14)60087-4

数学物理学报(英文版) ›› 2014, Vol. 34 ›› Issue (4): 1331-1344.doi: 10.1016/S0252-9602(14)60087-4

A NOTE ON SINGULAR INTEGRALS WITH DOMINATING MIXED SMOOTHNESS IN TRIEBEL-LIZORKIN SPACES

Hung Viet LE

Faculty of Science and Technology, Hoa Sen University, Quang Trung Software Park, Section 10, Ward Tan Chanh Hiep, District 12, Ho Chi Minh City, Viet Nam

收稿日期:2012-01-06 修回日期:2013-04-02 出版日期:2014-07-20 发布日期:2014-07-20

A NOTE ON SINGULAR INTEGRALS WITH DOMINATING MIXED SMOOTHNESS IN TRIEBEL-LIZORKIN SPACES

Hung Viet LE

Faculty of Science and Technology, Hoa Sen University, Quang Trung Software Park, Section 10, Ward Tan Chanh Hiep, District 12, Ho Chi Minh City, Viet Nam

Received:2012-01-06 Revised:2013-04-02 Online:2014-07-20 Published:2014-07-20

摘要/Abstract

摘要：

Let h be a measurable function defined on R⁺×R⁺. Let Ω∈ L(log L⁺)^ν_q (Sⁿ¹⁻¹×Sⁿ²⁻¹) (1 ≤ ν_q ≤2) be homogeneous of degree zero and satisfy certain cancellation condi-tions. We show that the singular integral

Tf(x₁, x₂) = p. v.∫∫_Rn1+n2Ω(y´₁, y´₂)h(|y₁|, |y₂|)/|y₁|ⁿ¹ |y₂|ⁿ²f(x₁ − y₁, x₂ − y₂)dy₁dy₂maps from S^α_¹, ^α^₂_{p, q}F(R^n₁ × R^n₂) boundedly to itself for 1 < p, q <∞, α₁, α₂ ∈R.

关键词: singular integrals, Marcinkiewicz integrals, mixed smoothness, Triebel-Lizorkin spaces

Abstract:

Key words: singular integrals, Marcinkiewicz integrals, mixed smoothness, Triebel-Lizorkin spaces

中图分类号:

42B20

Hung Viet LE. A NOTE ON SINGULAR INTEGRALS WITH DOMINATING MIXED SMOOTHNESS IN TRIEBEL-LIZORKIN SPACES[J]. 数学物理学报(英文版), 2014, 34(4): 1331-1344.

Hung Viet LE. A NOTE ON SINGULAR INTEGRALS WITH DOMINATING MIXED SMOOTHNESS IN TRIEBEL-LIZORKIN SPACES[J]. Acta mathematica scientia,Series B, 2014, 34(4): 1331-1344.

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A NOTE ON SINGULAR INTEGRALS WITH DOMINATING MIXED SMOOTHNESS IN TRIEBEL-LIZORKIN SPACES

A NOTE ON SINGULAR INTEGRALS WITH DOMINATING MIXED SMOOTHNESS IN TRIEBEL-LIZORKIN SPACES

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