# Gaussian integral means in the Fock space

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### Article Info

DATE

2021-12-17

AUTHORS ABSTRACT

We explore the relation between Hadamard products of two entire functions in the weighted Fock space Fγp\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathrm {F}^p_\gamma$$\end{document} and their integral Gaussian means. By introducing the key auxiliary function κγ,r\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\kappa _{\gamma ,r}$$\end{document}, we show that the growth of the Gaussian means of the Hadamard product f∗g∗κγ,r\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$f*g*\kappa _{\gamma ,r}$$\end{document} is controlled by the growth of Gaussian means of f and g. Among several consequences of this observation, in particular, we establish the sub-multiplicative property f∗g∗κF1≤‖f‖F1‖g‖F1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left\| f*g*\kappa \right\| _{\mathrm {F}^1}\le \Vert f\Vert _{\mathrm {F}^1}\Vert g\Vert _{\mathrm {F}^1}$$\end{document} for functions in the classical Fock space F1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathrm {F}^1$$\end{document}. More... »

PAGES

51

### References to SciGraph publications

• 1932-12. Some properties of fractional integrals. II in MATHEMATISCHE ZEITSCHRIFT
• 1899. Théorème sur les séries entières in ACTA MATHEMATICA
• 2013-11-07. Gaussian Integral Means of Entire Functions in COMPLEX ANALYSIS AND OPERATOR THEORY
• 2019-12-06. Differentiable families of traceless matrix triples in REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS, FÍSICAS Y NATURALES. SERIE A. MATEMÁTICAS
• 2012. Analysis on Fock Spaces in NONE
• 2020-02-17. Resolvent growth condition for composition operators on the Fock space in ANNALS OF FUNCTIONAL ANALYSIS

### Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s13398-021-01196-z

DOI

http://dx.doi.org/10.1007/s13398-021-01196-z

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https://app.dimensions.ai/details/publication/pub.1143969325

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