A MARCINKIEWICZ INTEGRAL TYPE CHARACTERIZATION OF THE SOBOLEV SPACE

作者：Hajlasz Piotr^*; Liu Zhuomin

来源：Publicacions Matematiques, 2017, 61(1): 83-104.

DOI：10.5565/PUBLMAT_61117_03

• Sobolev spaces
• Littlewood(_)Paley theory

In this paper we present a new characterization of the Sobolev space W-1,W- p , 1 < p < infinity which is a higher dimensional version of a result of Waterman [32]. We also provide a new and simplified proof of a recent result of Alabern, Mateu, and Verdera [2]. Finally, we generalize the results to the case of weighted Sobolev spaces with respect to a Muckenhoupt weight. 2010 Mathematics Subject Classification: Primary: 46E35; Secondary: 42B25.

• 出版日期2017