Abstract
We establish the most general Szasz type estimates for homogeneous Besov and Lizorkin-Triebel spaces, and their realizations.
Similar content being viewed by others
References
Bourdaud, G.: Realizations of homogeneous Besov and Lizorkin-Triebel spaces. Math. Nachr. 286, 476–491 (2013)
Bourdaud, G., Moussai, M., Sickel, W.: Composition operators in Lizorkin-Triebel spaces. J. Funct. Anal. 259, 1098–1128 (2010)
Jawerth, B.: Some observations on Besov and Lizorkin-Triebel spaces. Math. Scand. 40, 94–104 (1977)
Kaufmann, R.: On the theorem of Jarník and Besicovitch. Acta Arithm. 39, 265–267 (1981)
Moussai, M.: Composition operators on Besov algebras. Rev. Mat. Iberoam. 28, 239–272 (2012)
Moussai, M.: Realizations of homogeneous Besov and Triebel-Lizorkin spaces and an application to pointwise multipliers. Anal. Appl. (Singap.) 13, 149–183 (2015)
Peetre, J.: New Thoughts on Besov Spaces. Duke Univ. Math. Series I, Durham, N.C. (1976)
Runst, T., Sickel, W.: Sobolev Spaces of Fractional Order, Nemytskij Operators, and Nonlinear Partial Differential Equations. De Gruyter Series in Nonlinear Analysis and Applications, 3. Walter de Gruyter & Co., Berlin (1996)
Wolff, T.H.: Lectures on Harmonic Analysis. With a foreword by Charles Fefferman and a preface by Izabella Łaba. Edited by Łaba and Carol Shubin. University Lecture Series, 29. American Mathematical Society, Providence, RI (2003)
Yamazaki, M.: A quasihomogeneous version of paradifferential operators. I. Boundedness on spaces of Besov type. J. Fac. Sci. Univ. Tokyo, Sect. IA Math. 33 (1986), 131–174. II: A Symbolic calculus. ibidem 33 (1986), 311–345
Acknowledgements
I am grateful to Madani Moussai, who suggested to me this subject of research, and sent to me his preliminary works. I thank Hervé Quéffelec and Winfried Sickel for useful discussions in the preparation of the paper.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Bourdaud, G. Szasz’s theorem and its generalizations. Arch. Math. 118, 79–90 (2022). https://doi.org/10.1007/s00013-021-01664-3
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00013-021-01664-3