A Generalization of Exponential Class and Its Applications

作者：Gao Hongya^*; Liu Chao; Tian Hong

来源：Abstract and Applied Analysis, 2013, 2013: 476309.

DOI：10.1155/2013/476309

A function space, L-theta,L-infinity)(Omega), 0 <= theta < infinity, is defined. It is proved that L-theta,L-infinity)(Omega) is a Banach space which is a generalization of exponential class. An alternative definition of L-theta,L-infinity)(Omega) space is given. As an application, we obtain weak monotonicity property for very weak solutions of A-harmonic equation with variable coefficients under some suitable conditions related to L-theta,L-infinity) (Omega), which provides a generalization of a known result due toMoscariello. A weighted space L-w(theta,infinity)) (Omega) is also defined, and the boundedness for the Hardy- Littlewood maximal operator M-w and a Calderon-Zygmund operator T with respect to L-w(theta,infinity)) (Omega) is obtained.

• 出版日期2013
• 单位河北大学