Generalized Sobolev Spaces of Exponential Type Associated with the Dunkl Operators
2000 Mathematics Subject Classification: 35E45 In this paper we study generalized Sobolev spaces H^sG of exponential type associated with the Dunkl operators based on the space G of test functions for generalized hyperfunctions and investigate their properties. Moreover, we introduce a class of symbols of exponential type and their associated pseudodifferential operators related to the Dunkl operators, which act naturally on H^sG.