Weak Estimates of Singular Integrals with Variable Kernel and Fractional Differentiation on Morrey-Herz Spaces
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⁎-...
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| Format: | Article |
| Language: | English |
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Wiley
2017-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2017/4340805 |
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| author | Yanqi Yang Shuangping Tao |
| author_facet | Yanqi Yang Shuangping Tao |
| author_sort | Yanqi Yang |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-7afe3aa3f345429f8f1e7b7ffce1e091 |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2017-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-7afe3aa3f345429f8f1e7b7ffce1e0912025-02-03T06:12:44ZengWileyJournal of Function Spaces2314-88962314-88882017-01-01201710.1155/2017/43408054340805Weak Estimates of Singular Integrals with Variable Kernel and Fractional Differentiation on Morrey-Herz SpacesYanqi Yang0Shuangping Tao1College of Mathematics and Statistics, Northwest Normal University, Lanzhou, Gansu 730070, ChinaCollege of Mathematics and Statistics, Northwest Normal University, Lanzhou, Gansu 730070, ChinaLet 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.http://dx.doi.org/10.1155/2017/4340805 |
| spellingShingle | Yanqi Yang Shuangping Tao Weak Estimates of Singular Integrals with Variable Kernel and Fractional Differentiation on Morrey-Herz Spaces Journal of Function Spaces |
| title | Weak Estimates of Singular Integrals with Variable Kernel and Fractional Differentiation on Morrey-Herz Spaces |
| title_full | Weak Estimates of Singular Integrals with Variable Kernel and Fractional Differentiation on Morrey-Herz Spaces |
| title_fullStr | Weak Estimates of Singular Integrals with Variable Kernel and Fractional Differentiation on Morrey-Herz Spaces |
| title_full_unstemmed | Weak Estimates of Singular Integrals with Variable Kernel and Fractional Differentiation on Morrey-Herz Spaces |
| title_short | Weak Estimates of Singular Integrals with Variable Kernel and Fractional Differentiation on Morrey-Herz Spaces |
| title_sort | weak estimates of singular integrals with variable kernel and fractional differentiation on morrey herz spaces |
| url | http://dx.doi.org/10.1155/2017/4340805 |
| work_keys_str_mv | AT yanqiyang weakestimatesofsingularintegralswithvariablekernelandfractionaldifferentiationonmorreyherzspaces AT shuangpingtao weakestimatesofsingularintegralswithvariablekernelandfractionaldifferentiationonmorreyherzspaces |