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• 1 Indian Institute of Technology Madras Department of Mathematics Chennai 600 036 India
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Abstract

In this paper, it is shown that the class of right Fourier multipliers for the Sobolev space Wk,p(Hn) coincides with the class of right Fourier multipliers for Lp(Hn) for k ∈ ℕ, 1 < p < ∞. Towards this end, it is shown that the operators Rj
\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\bar R$$ \end{document}
j−1 and
\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\bar R$$ \end{document}
jRj−1 are bounded on Lp(Hn), 1 < p < ∞, where
\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$R_j = \frac{\partial } {{\partial z_j }} - \frac{i} {4}\bar z_j \frac{\partial } {{\partial t}}, \bar R_j = \frac{\partial } {{\partial \bar z_j }} + \frac{i} {4}z_j \frac{\partial } {{\partial t}}$$ \end{document}
and ℒ is the sublaplacian on Hn. This proof is based on the Calderon-Zygmund theory on the Heisenberg group. It is also shown that when p = 1, the class of right multipliers for the Sobolev space Wk,1(Hn) coincides with the dual space of the projective tensor product of two function spaces.

• Impact Factor (2019): 0.527
• Scimago Journal Rank (2019): 0.384
• SJR Hirsch-Index (2019): 15
• SJR Quartile Score (2019): Q3 Analysis
• SJR Quartile Score (2019): Q3 Mathematics (miscellaneous)
• Impact Factor (2018): 0.702
• Scimago Journal Rank (2018): 0.47
• SJR Hirsch-Index (2018): 14
• SJR Quartile Score (2018): Q2 Mathematics (miscellaneous)

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Analysis Mathematica
Language English
Size B5
Year of
Foundation
1975
Volumes
per Year
1
Issues
per Year
4
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H-1117 Budapest, Hungary 1516 Budapest, PO Box 245
Springer Nature Switzerland AG
Publisher's
H-1117 Budapest, Hungary 1516 Budapest, PO Box 245.
CH-6330 Cham, Switzerland Gewerbestrasse 11.
Responsible
Publisher
ISSN 0133-3852 (Print)
ISSN 1588-273X (Online)

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