Weighted boundedness of Toeplitz type operators related to singular integral operators with non-smooth kernel

Xiaosha Zhou; Lanzhe Liu

Xiaosha Zhou ; Lanzhe Liu

Colloquium Mathematicae, Tome 131 (2013), p. 253-271 / Harvested from The Polish Digital Mathematics Library

Résumé

Some weighted sharp maximal function inequalities for the Toeplitz type operator $T_{b} = \sum_{k = 1}^{m} T^{k, 1} M_{b} T^{k, 2}$ are established, where $T^{k, 1}$ are a fixed singular integral operator with non-smooth kernel or ±I (the identity operator), $T^{k, 2}$ are linear operators defined on the space of locally integrable functions, k = 1,..., m, and $M_{b} (f) = b f$ . The weighted boundedness of $T_{b}$ on Morrey spaces is obtained by using sharp maximal function inequalities.

Publié le : 2013-01-01

Zbl 1284.42051

EUDML-ID : urn:eudml:doc:283465

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     author = {Xiaosha Zhou and Lanzhe Liu},
     title = {Weighted boundedness of Toeplitz type operators related to singular integral operators with non-smooth kernel},
     journal = {Colloquium Mathematicae},
     volume = {131},
     year = {2013},
     pages = {253-271},
     zbl = {1284.42051},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm133-2-12}
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Xiaosha Zhou; Lanzhe Liu. Weighted boundedness of Toeplitz type operators related to singular integral operators with non-smooth kernel. Colloquium Mathematicae, Tome 131 (2013) pp. 253-271. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm133-2-12/