Arkiv för Matematik

  • Ark. Mat.
  • Volume 44, Number 2 (2006), 241-259.

Boundedness for pseudodifferential operators on multivariate α-modulation spaces

Lasse Borup and Morten Nielsen

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Abstract

The α-modulation spaces Msp, q(Rd), 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 Sbρ,0 extends to a bounded operator σ(x, D): Msp, q(Rd)→Ms-bp, q(Rd) provided 0≤α≤ρ≤1, and 1< p, q<∞. The result extends the well-known result that pseudodifferential operators with symbol in the class Sb1,0 maps the Besov space Bsp, q(Rd) into Bs-bp, q(Rd).

Article information

Source
Ark. Mat. Volume 44, Number 2 (2006), 241-259.

Dates
Received: 22 February 2005
Revised: 23 September 2005
First available in Project Euclid: 31 January 2017

Permanent link to this document
http://projecteuclid.org/euclid.afm/1485898954

Digital Object Identifier
doi:10.1007/s11512-006-0020-y

Zentralblatt MATH identifier
1170.35562

Rights
2006 © Institut Mittag-Leffler

Citation

Borup, Lasse; Nielsen, Morten. Boundedness for pseudodifferential operators on multivariate α-modulation spaces. Ark. Mat. 44 (2006), no. 2, 241--259. doi:10.1007/s11512-006-0020-y. http://projecteuclid.org/euclid.afm/1485898954.


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