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Generalized Cesàro operators on certain function spaces

100%

Naik S.

Annales Polonici Mathematici

2010

tom 98

nr 2

189-199

Motivated by some recent results by Li and Stević, in this paper we prove that a two-parameter family of Cesàro averaging operators $𝓟^{b,c}$ is bounded on the Dirichlet spaces $𝓓_{p,a}$. We also give a short and direct proof of boundedness of $𝓟^{b,c}$ on the Hardy space $H^p$ for 1 < p < ∞.

Generalized Hilbert Operators on Bergman and Dirichlet Spaces of Analytic Functions

63%

Naik S., Rajbangshi K.

Bulletin of the Polish Academy of Sciences. Mathematics

2015

tom 63

nr 3

227-235

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).

Ograniczanie wyników

1 Annales Polonici Mathematici

1 Bulletin of the Polish Academy of Sciences. Mathematics

2 Naik S.

1 Rajbangshi K.

1 2015

1 2010

Wyniki wyszukiwania

Generalized Cesàro operators on certain function spaces

Generalized Hilbert Operators on Bergman and Dirichlet Spaces of Analytic Functions