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

Xiaosha Zhou; Lanzhe Liu

Colloquium Mathematicae (2013)

  • Volume: 133, Issue: 2, page 253-271
  • ISSN: 0010-1354

Abstract

top
Some weighted sharp maximal function inequalities for the Toeplitz type operator T b = ∑ 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.

How to cite

top

Xiaosha Zhou, and Lanzhe Liu. "Weighted boundedness of Toeplitz type operators related to singular integral operators with non-smooth kernel." Colloquium Mathematicae 133.2 (2013): 253-271. <http://eudml.org/doc/283465>.

@article{XiaoshaZhou2013,
abstract = {Some weighted sharp maximal function inequalities for the Toeplitz type operator $T_b = ∑_\{k= 1\}^\{m\} T^\{k,1\}M_bT^\{k,2\}$ 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 $M_b(f) = bf$. The weighted boundedness of $T_b$ on Morrey spaces is obtained by using sharp maximal function inequalities.},
author = {Xiaosha Zhou, Lanzhe Liu},
journal = {Colloquium Mathematicae},
keywords = {Toeplitz type operator; singular integral operator; sharp maximal function; Morrey space; weighted BMO; weighted Lipschitz function},
language = {eng},
number = {2},
pages = {253-271},
title = {Weighted boundedness of Toeplitz type operators related to singular integral operators with non-smooth kernel},
url = {http://eudml.org/doc/283465},
volume = {133},
year = {2013},
}

TY - JOUR
AU - Xiaosha Zhou
AU - Lanzhe Liu
TI - Weighted boundedness of Toeplitz type operators related to singular integral operators with non-smooth kernel
JO - Colloquium Mathematicae
PY - 2013
VL - 133
IS - 2
SP - 253
EP - 271
AB - Some weighted sharp maximal function inequalities for the Toeplitz type operator $T_b = ∑_{k= 1}^{m} T^{k,1}M_bT^{k,2}$ 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 $M_b(f) = bf$. The weighted boundedness of $T_b$ on Morrey spaces is obtained by using sharp maximal function inequalities.
LA - eng
KW - Toeplitz type operator; singular integral operator; sharp maximal function; Morrey space; weighted BMO; weighted Lipschitz function
UR - http://eudml.org/doc/283465
ER -

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.