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Abstrakty
Let f be an analytic function on the unit disk 𝔻. We define a generalized Hilbert-type operator $𝓗_{a,b}$ by
$𝓗_{a,b}(f)(z) = Γ(a+1)/Γ(b+1) ∫_{0}^{1} (f(t)(1-t)^{b})/((1-tz)^{a+1}) dt$,
where a and b are non-negative real numbers. In particular, for a = b = β, $𝓗_{a,b}$ becomes the generalized Hilbert operator $𝓗_β$, and β = 0 gives the classical Hilbert operator 𝓗. In this article, we find conditions on a and b such that $𝓗_{a,b}$ is bounded on Dirichlet-type spaces $S^{p}$, 0 < p < 2, and on Bergman spaces $A^{p}$, 2 < p < ∞. Also we find an upper bound for the norm of the operator $𝓗_{a,b}$. These generalize some results of E. Diamantopolous (2004) and S. Li (2009).
$𝓗_{a,b}(f)(z) = Γ(a+1)/Γ(b+1) ∫_{0}^{1} (f(t)(1-t)^{b})/((1-tz)^{a+1}) dt$,
where a and b are non-negative real numbers. In particular, for a = b = β, $𝓗_{a,b}$ becomes the generalized Hilbert operator $𝓗_β$, and β = 0 gives the classical Hilbert operator 𝓗. In this article, we find conditions on a and b such that $𝓗_{a,b}$ is bounded on Dirichlet-type spaces $S^{p}$, 0 < p < 2, and on Bergman spaces $A^{p}$, 2 < p < ∞. Also we find an upper bound for the norm of the operator $𝓗_{a,b}$. These generalize some results of E. Diamantopolous (2004) and S. Li (2009).
Słowa kluczowe
Kategorie tematyczne
Rocznik
Tom
Numer
Strony
227-235
Opis fizyczny
Daty
wydano
2015
Twórcy
autor
- Department of Applied Sciences, Gauhati University, Guwahati 781-014, India
autor
- Department of Applied Sciences, Gauhati University, Guwahati 781-014, India
Bibliografia
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Bibliografia
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Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_4064-ba8031-1-2016