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Volume 27, Issue 1
Boundedness of Parabolic Singular Integrals and Marcinkiewicz Integrals on Triebel-Lizorkin Spaces

Y. M. Niu & S. P. Tao

Anal. Theory Appl., 27 (2011), pp. 59-75.

Published online: 2011-01

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  • Abstract

In this paper, we obtain the boundedness of the parabolic singular integral operator $T$ with kernel in $L(\log L)^{1/ \gamma} (S^{n−1})$ on Triebel-Lizorkin spaces. Moreover, we prove the boundedness of a class of Marcinkiewicz integrals $\mu_{\Omega,q}(f)$ from $\|f\|_{\dot{F}_{p}^{0,q}(\mathbf{R}^n)}$ into $L^p(\mathbf{R}^n)$.

  • AMS Subject Headings

42B25, 42B35

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{ATA-27-59, author = {}, title = {Boundedness of Parabolic Singular Integrals and Marcinkiewicz Integrals on Triebel-Lizorkin Spaces}, journal = {Analysis in Theory and Applications}, year = {2011}, volume = {27}, number = {1}, pages = {59--75}, abstract = {

In this paper, we obtain the boundedness of the parabolic singular integral operator $T$ with kernel in $L(\log L)^{1/ \gamma} (S^{n−1})$ on Triebel-Lizorkin spaces. Moreover, we prove the boundedness of a class of Marcinkiewicz integrals $\mu_{\Omega,q}(f)$ from $\|f\|_{\dot{F}_{p}^{0,q}(\mathbf{R}^n)}$ into $L^p(\mathbf{R}^n)$.

}, issn = {1573-8175}, doi = {https://doi.org/10.1007/s10496-011-0059-x}, url = {http://global-sci.org/intro/article_detail/ata/4580.html} }
TY - JOUR T1 - Boundedness of Parabolic Singular Integrals and Marcinkiewicz Integrals on Triebel-Lizorkin Spaces JO - Analysis in Theory and Applications VL - 1 SP - 59 EP - 75 PY - 2011 DA - 2011/01 SN - 27 DO - http://doi.org/10.1007/s10496-011-0059-x UR - https://global-sci.org/intro/article_detail/ata/4580.html KW - parabolic singular integral, Triebel-Lizorkin space, Marcinkiewica integral, rough kernel. AB -

In this paper, we obtain the boundedness of the parabolic singular integral operator $T$ with kernel in $L(\log L)^{1/ \gamma} (S^{n−1})$ on Triebel-Lizorkin spaces. Moreover, we prove the boundedness of a class of Marcinkiewicz integrals $\mu_{\Omega,q}(f)$ from $\|f\|_{\dot{F}_{p}^{0,q}(\mathbf{R}^n)}$ into $L^p(\mathbf{R}^n)$.

Y. M. Niu & S. P. Tao. (1970). Boundedness of Parabolic Singular Integrals and Marcinkiewicz Integrals on Triebel-Lizorkin Spaces. Analysis in Theory and Applications. 27 (1). 59-75. doi:10.1007/s10496-011-0059-x
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