On Lorentz mixed normed modulation spaces

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Sandıkçı A.

JOURNAL OF PSEUDO-DIFFERENTIAL OPERATORS AND APPLICATIONS, vol.3, no.3, pp.263-281, 2012 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 3 Issue: 3
  • Publication Date: 2012
  • Doi Number: 10.1007/s11868-012-0051-z
  • Journal Name: JOURNAL OF PSEUDO-DIFFERENTIAL OPERATORS AND APPLICATIONS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.263-281
  • Keywords: Gabor transform, Lorentz mixed norm space, modulation space, Weyl operator, Multiplier, TIME-FREQUENCY ANALYSIS, MULTIPLIERS, LP
  • Ondokuz Mayıs University Affiliated: Yes

Abstract

This paper is a study on a new kind modulation spaces M(P, Q)(R-d) and A(P, Q, r)(R-d) for indices in the range 1 < P < infinity, 1 <= Q < infinity and 1 <= r < infinity, modelled on Lorentz mixed norm spaces instead of mixed norm L-P spaces as the spaces M-m(p,q) (R-d) (Feichtinger in Modulation spaces on locally compact Abelian groups, 1983; Grochenig in Foundations of Time-Frequency Analysis. Birkh auser, Boston, 2001), and Lorentz spaces as the spaces M(p, q)(R-d) (Gurkanhin J Math Kyoto Univ 46:595-616, 2006). First, we prove the main properties of these spaces. Later, we describe the dual spaces and determine the multiplier spaces for both of them. Moreover, we investigate the boundedness of Weyl operators and localization operators on M(P, Q)(R-d). Finally, we give an interpolation theorem for M(P, Q)(R-d).