Skip to main content Accessibility help




The goal of this paper is to characterize the operating functions on modulation spaces $M^{p,1}(\mathbb{R})$ and Wiener amalgam spaces $W^{p,1}(\mathbb{R})$ . This characterization gives an affirmative answer to the open problem proposed by Bhimani (Composition Operators on Wiener amalgam Spaces, arXiv: 1503.01606) and Bhimani and Ratnakumar (J. Funct. Anal. 270 (2016), pp. 621–648).



Hide All
[1] Bényi, A. and Oh, T., Modulation spaces, Wiener amalgam spaces, and Brownian motions , Adv. Math. 228 (2011), 29432981.
[2] Bhimani, D. G., Composition operators on Wiener amalgam spaces, preprint, 2015,arXiv:1503.01606.
[3] Bhimani, D. G. and Ratnakumar, P. K., Functions operating on modulation spaces and nonlinear dispersive equations , J. Funct. Anal. 270 (2016), 621648.
[4] Feichtinger, H. G., “ Modulation spaces on locally compact abelian groups ”, in Wavelets and their Applications, (eds. Krishna, M., Radha, R. and Thangavelu, S.) Chennai, India, Allied Publishers, New Delhi, 2003, 99140. Updated version of a technical report, University of Vienna, 1983.
[5] Gröchenig, K., Foundations of Time-Frequency Analysis, Birkhäuser, Boston, 2001.
[6] Helson, H., Kahane, J. P., Katznelson, Y. and Rudin, W., The functions which operate on Fourier transforms , Acta Math. 102 (1959), 135157.
[7] Kahane, J. P., Series de Fourier Absolument Convergentes, Springer, Berlin–Heidelberg–New york, 1970.
[8] Katznelson, Y., An Introduction to Harmonic Analysis, Second corrected edition Dover Publications, Inc, New York, 1976.
[9] Lévy, P., Sur la convergence absolue des series de Fourier , Compos. Math. 1 (1935), 114.
[10] Rudin, W., Fourier Analysis on Groups, Interscience Tracts in Pure and Applied Mathematics, Interscience Publishers, New York–London, 1962.
[11] Ruzhansky, M., Sugimoto, M. and Wang, B., “ Modulation spaces and nonlinear evolution equations ”, in Evolution Equations of Hyperbolic and Schrodinger Type, 267–283, Progr. Math., 301 , Springer Basel AG, Basel, Birkhäuser, 2012.
[12] Sugimoto, M. and Tomita, N., The dilation property of modulation spaces and their inclusion relation with Besov spaces , J. Funct. Anal. 248 (2007), 79106.
[13] Toft, J., Continuity properties for modulation spaces, with applications to pseudo-differential calculus. I , J. Funct. Anal. 207 (2004), 399429.
[14] Toft, J., Pseudo-differential operators with smooth symbols on modulation spaces , Cubo 11 (2009), 87107.
[15] Wiener, N., Tauberian theorems , Ann. of Math. (2) 33 (1932), 1100.
MathJax is a JavaScript display engine for mathematics. For more information see

MSC classification


Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed