Characterizations of some operators on the vanishing generalized Morrey spaces with variable exponent

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• 作者：Pinhong Long ; ^{hnlphlch10601@sina.com" class="auth_mail" title="E-mail the corresponding author} ; Huili Han ^{nxhan@126.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Variable exponent ; Vanishing Morrey space ; Maximal operator ; Potential operator ; Singular integral operator
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2016
• 出版时间：1 May 2016
• 年：2016
• 卷：437
• 期：1
• 页码：419-430
• 全文大小：372 K

文摘

In this paper we will give some characterizations for the boundedness of the maximal operators, potential operators and singular integral operators on the vanishing generalized Morrey spaces $V{\mathcal{L}}_{\mathrm{\Pi }}^{p(\cdot ),\phi }(\mathrm{\Omega })$ with variable exponent p(⋅)$p(\cdot )$ and bounded set Ω. Moreover, we also obtain some corresponding results for unbounded set Ω on such these spaces.