Vector Valued Inequalities for Fourier Series

1980 ◽  
Vol 78 (4) ◽  
pp. 525 ◽  
Author(s):  
Jose L. Rubio De Francia
Keyword(s):  
Fourier Series ◽  
Vector Valued

scholarly journals On the growth of vector-valued Fourier series

2013 ◽  
Vol 62 (6) ◽  
pp. 1765-1784
Author(s):  
Javier Parcet ◽  
Fernando Soria ◽  
Quanhua Xu
Keyword(s):  
Fourier Series ◽  
Vector Valued

scholarly journals Pointwise convergence of vector-valued Fourier series

2013 ◽  
Vol 357 (4) ◽  
pp. 1329-1361 ◽  
Author(s):  
Tuomas P. Hytönen ◽  
Michael T. Lacey
Keyword(s):  
Fourier Series ◽  
Pointwise Convergence ◽  
Vector Valued

scholarly journals A variation norm Carleson theorem for vector-valued Walsh–Fourier series

2014 ◽  
Vol 30 (3) ◽  
pp. 979-1014 ◽  
Author(s):  
Tuomas Hytönen ◽  
Michael Lacey ◽  
Ioannis Parissis
Keyword(s):  
Fourier Series ◽  
Variation Norm ◽  
Vector Valued

Two new spaces of vector-valued limit power functions

2007 ◽  
Vol 44 (4) ◽  
pp. 423-443 ◽  
Author(s):  
Chuanyi Zhang ◽  
Chenhui Meng
Keyword(s):  
Fourier Series ◽  
Power Function ◽  
Hilbert Spaces ◽  
Almost Periodic ◽  
Periodic Functions ◽  
Power Functions ◽  
Uniform Limit ◽  
Parseval’S Equality ◽  
Vector Valued ◽  
Limit Power

To answer a question in [24], we propose \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} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\mathcal{U}\mathcal{L}\mathcal{P}(\mathbb{R}^ + ,H)$$ \end{document}, the space of uniform limit power functions 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} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\mathcal{L}\mathcal{P}_2$$ \end{document}, the space of limit power functions. We show that \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} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\mathcal{U}\mathcal{L}\mathcal{P}(\mathbb{R}^ + ,H)$$ \end{document} 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} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\mathcal{L}\mathcal{P}_2$$ \end{document} have properties respectively similar to that of \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} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\mathcal{A}\mathcal{P}(\mathbb{R}^ + ,H)$$ \end{document}, the space of almost periodic functions and to that of B2 , Besicovitch’s space. Finally, we point out that \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} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\mathcal{L}\mathcal{P}_2$$ \end{document} is the largest among those Hilbert spaces in limit power function set whose members have associated Fourier series (in the sense of a new basis) and satisfy Parseval’s equality.

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