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Weak Estimates of Singular Integrals with Variable Kernel and Fractional Differentiation on Morrey-Herz Spaces
Joint Authors
Source
Issue
Vol. 2017, Issue 2017 (31 Dec. 2017), pp.1-10, 10 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2017-12-31
Country of Publication
Egypt
No. of Pages
10
Main Subjects
Abstract EN
Let T be the singular integral operator with variable kernel defined by Tf(x)=p.v.∫Rn(Ω(x,x-y)/x-yn)f(y)dy and let Dγ (0≤γ≤1) be the fractional differentiation operator.
Let T⁎and T♯ be the adjoint of T and the pseudoadjoint of T, respectively.
In this paper, the authors prove that TDγ-DγT and (T⁎-T♯)Dγ are bounded, respectively, from Morrey-Herz spaces MK˙p,1α,λ(Rn) to the weak Morrey-Herz spaces WMK˙p,1α,λ(Rn) by using the spherical harmonic decomposition.
Furthermore, several norm inequalities for the product T1T2 and the pseudoproduct T1∘T2 are also given.
American Psychological Association (APA)
Yang, Yanqi& Tao, Shuangping. 2017. Weak Estimates of Singular Integrals with Variable Kernel and Fractional Differentiation on Morrey-Herz Spaces. Journal of Function Spaces،Vol. 2017, no. 2017, pp.1-10.
https://search.emarefa.net/detail/BIM-1176453
Modern Language Association (MLA)
Yang, Yanqi& Tao, Shuangping. Weak Estimates of Singular Integrals with Variable Kernel and Fractional Differentiation on Morrey-Herz Spaces. Journal of Function Spaces No. 2017 (2017), pp.1-10.
https://search.emarefa.net/detail/BIM-1176453
American Medical Association (AMA)
Yang, Yanqi& Tao, Shuangping. Weak Estimates of Singular Integrals with Variable Kernel and Fractional Differentiation on Morrey-Herz Spaces. Journal of Function Spaces. 2017. Vol. 2017, no. 2017, pp.1-10.
https://search.emarefa.net/detail/BIM-1176453
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1176453