Affiliation:
1. Department of Mathematics, Tokyo University of Science, Kagurazaka 1-3, Shinjuku-ku, Tokyo 162-8601, Japan
Abstract
The purpose of this paper is to construct modulation spacesMp,q(Rd)for general0<p,q≦∞, which coincide with the usual modulation spaces when1≦p,q≦∞, and study their basic properties including their completeness. Given anyg∈S(Rd)such that suppĝ⊂ {ξ∣|ξ|≦1}and∑k∈Zdĝ(ξ-αk)≡1, our modulation space consists of all tempered distributionsfsuch that the (quasi)-norm‖f‖M[g]p,q:≔(∫Rd(∫Rd|f*(Mωg)(x)|pdx)qpdω)1qis finite.
Cited by
43 articles.
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