Abstract
We define and study the Lorentz spaces associated with the Dunkl operators onℝd. Furthermore, we obtain the Strichartz estimates for the Dunkl-Schrödinger equations under the generalized Lorentz norms. The Sobolev inequalities between the homogeneous Dunkl-Besov spaces and generalized Lorentz spaces are also considered.
Highlights
Dunkl operators Tj (j = 1, . . . , d) introduced by Dunkl in [1] are parameterized differential-difference operators on Rd that are related to finite reflection groups
Dunkl operators are naturally connected with certain Schrodinger operators for Calogero-Sutherlandtype quantum many-body systems [2,3,4]
We intend to continue our study of generalized spaces of type Sobolev associated with Dunkl operators started in [12, 13]
Summary
Much attention has been paid to these operators in various mathematical (and even physical) directions In this prospect, Dunkl operators are naturally connected with certain Schrodinger operators for Calogero-Sutherlandtype quantum many-body systems [2,3,4]. We intend to continue our study of generalized spaces of type Sobolev associated with Dunkl operators started in [12, 13]. We establish Sobolev inequalities between the homogeneous Dunkl-Besov spaces and generalized Lorentz spaces, and we give many applications
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