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A Generalization of Exponential Class and Its Applications

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  • Hongya Gao
  • Chao Liu
  • Hong Tian

Abstract

A function space, , , is defined. It is proved that is a Banach space which is a generalization of exponential class. An alternative definition of space is given. As an application, we obtain weak monotonicity property for very weak solutions of -harmonic equation with variable coefficients under some suitable conditions related to , which provides a generalization of a known result due to Moscariello. A weighted space is also defined, and the boundedness for the Hardy-Littlewood maximal operator and a Calderón-Zygmund operator with respect to is obtained.

Suggested Citation

  • Hongya Gao & Chao Liu & Hong Tian, 2013. "A Generalization of Exponential Class and Its Applications," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-8, June.
    • Handle: RePEc:hin:jnlaaa:476309
    DOI: 10.1155/2013/476309
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