IJPAM: Volume 107, No. 3 (2016)

COMPOSITION OPERATORS BETWEEN
WEIGHTED HARDY TYPE SPACES

Pawan Kumar$^1$, Zaheer Abbas$^2$
$^{1,2}$Department of Mathematical Sciences
Baba Ghulam Shah Badshah University, Rajouri
Jammu, INDIA


Abstract. Let $\varphi$ be an analytic self-map of the open unit disc $\mathbb {D}$ in the finite complex plane $\mathbb{C}$. Let $ C_{\varphi}\;, D $ be the composition and differentiation operators defined by $C_{\varphi}f=f\circ\varphi,~~~Df= f^{\prime} $ respectively. In this paper, we shall consider the operators $C_{\varphi}D$ and $DC_{\varphi}$ defined by $C_{\varphi}Df = f^{\prime}\circ \varphi $ and $DC_{\varphi}f= (f\circ \varphi)^{\prime}$ respectively and we shall discuss the boundedness and compactness of the operators $C_{\varphi}D$ and $DC_{\varphi}$ on weighted Hardy spaces by using the orthonormal basis of the weighted Hardy spaces.




Received: November 26, 2015

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DOI: 10.12732/ijpam.v107i3.6 How to cite this paper?

Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2016
Volume: 107
Issue: 3
Pages: 579 - 587


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