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Zapiski Nauchnykh Seminarov POMI, 2011, Volume 392, Pages 5–31 (Mi znsl4576)  
This article is cited in 1 scientific paper (total in 1 paper)

On the norms of generalized translation operators generated by Dunkl-type operators

O. L. Vinogradov

Saint-Petersburg State University, Saint-Petersburg, Russia
Full-text PDF (359 kB) Citations (1)
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Abstract: The paper establishes the integral representation and improves the norm estimate for the generalized translation operators generated by Dunkl-type operators
$$ \Lambda f(x)=f'(x)+\frac{A'(x)}{A(x)}\,\frac{f(x)-f(-x)}2 $$
in the spaces $L_p(\mathbb R)$ with weight $A$. Under some natural conditions on the function $A$, it is proved that these norms do not exceed two.
Key words and phrases: Bessel functions, generalized translation operator, Dunkl-type operators.
Received: 16.02.2011
English version:
Journal of Mathematical Sciences (New York), 2012, Volume 184, Issue 6, Pages 663–678
DOI: https://doi.org/10.1007/s10958-012-0889-x
Bibliographic databases:
Document Type: Article
UDC: 517.5
Language: Russian
Citation: O. L. Vinogradov, “On the norms of generalized translation operators generated by Dunkl-type operators”, Analytical theory of numbers and theory of functions. Part 26, Zap. Nauchn. Sem. POMI, 392, POMI, St. Petersburg, 2011, 5–31; J. Math. Sci. (N. Y.), 184:6 (2012), 663–678
Citation in format AMSBIB
\Bibitem{Vin11}
\by O.~L.~Vinogradov
\paper On the norms of generalized translation operators generated by Dunkl-type operators
\inbook Analytical theory of numbers and theory of functions. Part~26
\serial Zap. Nauchn. Sem. POMI
\yr 2011
\vol 392
\pages 5--31
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl4576}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2012
\vol 184
\issue 6
\pages 663--678
\crossref{https://doi.org/10.1007/s10958-012-0889-x}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84864285341}
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  • https://www.mathnet.ru/eng/znsl/v392/p5
    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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