On a Singular Integral of Christ–Journé Type with Homogeneous Kernel
Canadian mathematical bulletin, Tome 61 (2018) no. 1, pp. 97-113
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In this paper, we prove that the singular integral defined by ${{T}_{\Omega ,a}}f(x)=\text{p}\text{.}\text{v}\text{.}{{\int }_{{{\mathbb{R}}^{d}}}}\frac{\Omega (x-y)}{|x-y{{|}^{d}}}\cdot {{m}_{x,y}}a\cdot f(y)dy$ is bounded on ${{L}^{p}}({{\mathbb{R}}^{d}})$ for $1\,<\,p\,<\,\infty $ and is of weak type (1,1), where $\Omega \,\in L\text{lo}{{\text{g}}^{+}}L({{S}^{d-1}})$ and ${{m}_{x,y}}a\,=:\,\int{_{0}^{1}}\,a(sx\,+\,(1\,-\,s)y)ds$ , with $a\,\in \,{{L}^{\infty }}({{\mathbb{R}}^{d}})\,$ satisfying some restricted conditions.
Ding, Yong; Lai, Xudong. On a Singular Integral of Christ–Journé Type with Homogeneous Kernel. Canadian mathematical bulletin, Tome 61 (2018) no. 1, pp. 97-113. doi: 10.4153/CMB-2017-040-1
@article{10_4153_CMB_2017_040_1,
author = {Ding, Yong and Lai, Xudong},
title = {On a {Singular} {Integral} of {Christ{\textendash}Journ\'e} {Type} with {Homogeneous} {Kernel}},
journal = {Canadian mathematical bulletin},
pages = {97--113},
year = {2018},
volume = {61},
number = {1},
doi = {10.4153/CMB-2017-040-1},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2017-040-1/}
}
TY - JOUR AU - Ding, Yong AU - Lai, Xudong TI - On a Singular Integral of Christ–Journé Type with Homogeneous Kernel JO - Canadian mathematical bulletin PY - 2018 SP - 97 EP - 113 VL - 61 IS - 1 UR - http://geodesic.mathdoc.fr/articles/10.4153/CMB-2017-040-1/ DO - 10.4153/CMB-2017-040-1 ID - 10_4153_CMB_2017_040_1 ER -
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