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Boundedness for pseudodifferential operators on multivariate α-modulation spaces

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Arkiv för Matematik

Abstract

The α-modulation spaces M s,α p,q(R d), α∈[0,1], form a family of spaces that contain the Besov and modulation spaces as special cases. In this paper we prove that a pseudodifferential operator σ(x,D) with symbol in the Hörmander class S b ρ,0 extends to a bounded operator σ(x,D):M s,α p,q(R d)→M s-b,α p,q(R d) provided 0≤α≤ρ≤1, and 1<p,q<∞. The result extends the well-known result that pseudodifferential operators with symbol in the class S b 1,0 maps the Besov space B s p,q(R d) into B s-b p,q(R d).

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Authors and Affiliations

  1. Department of Mathematical Sciences, Aalborg University, Fredrik Bajers Vej 7G, DK-9220, Aalborg East, Denmark

    Lasse Borup

  2. Department of Mathematics, Washington University, Campus Box 1146, St. Louis, MO, 63130, USA

    Morten Nielsen

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  1. Lasse Borup
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  2. Morten Nielsen
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Correspondence to Lasse Borup.

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Borup, L., Nielsen, M. Boundedness for pseudodifferential operators on multivariate α-modulation spaces . Ark Mat 44, 241–259 (2006). https://doi.org/10.1007/s11512-006-0020-y

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  • DOI: https://doi.org/10.1007/s11512-006-0020-y

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