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Search: All articles in the CJM digital archive with keyword singular integral

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1. CJM 2011 (vol 64 pp. 257)

Chen, Yanping; Ding, Yong; Wang, Xinxia
Compactness of Commutators for Singular Integrals on Morrey Spaces
In this paper we characterize the compactness of the commutator $[b,T]$ for the singular integral operator on the Morrey spaces $L^{p,\lambda}(\mathbb R^n)$. More precisely, we prove that if $b\in \operatorname{VMO}(\mathbb R^n)$, the $\operatorname {BMO} (\mathbb R^n)$-closure of $C_c^\infty(\mathbb R^n)$, then $[b,T]$ is a compact operator on the Morrey spaces $L^{p,\lambda}(\mathbb R^n)$ for $1\lt p\lt \infty$ and $0\lt \lambda\lt n$. Conversely, if $b\in \operatorname{BMO}(\mathbb R^n)$ and $[b,T]$ is a compact operator on the $L^{p,\,\lambda}(\mathbb R^n)$ for some $p\ (1\lt p\lt \infty)$, then $b\in \operatorname {VMO}(\mathbb R^n)$. Moreover, the boundedness of a rough singular integral operator $T$ and its commutator $[b,T]$ on $L^{p,\,\lambda}(\mathbb R^n)$ are also given. We obtain a sufficient condition for a subset in Morrey space to be a strongly pre-compact set, which has interest in its own right.

Keywords:singular integral, commutators, compactness, VMO, Morrey space
Categories:42B20, 42B99

2. CJM 2009 (vol 62 pp. 202)

Tang, Lin
Interior $h^1$ Estimates for Parabolic Equations with $\operatorname{LMO}$ Coefficients
In this paper we establish \emph{a priori} $h^1$-estimates in a bounded domain for parabolic equations with vanishing $\operatorname{LMO}$ coefficients.

Keywords:parabolic operator, Hardy space, parabolic, singular integrals and commutators
Categories:35K20, 35B65, 35R05

3. CJM 2000 (vol 52 pp. 381)

Miyachi, Akihiko
Hardy Space Estimate for the Product of Singular Integrals
$H^p$ estimate for the multilinear operators which are finite sums of pointwise products of singular integrals and fractional integrals is given. An application to Sobolev space and some examples are also given.

Keywords:$H^p$ space, multilinear operator, singular integral, fractional integration, Sobolev space
Category:42B20

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