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A STUDY OF SLANT WEIGHTED TOEPLITZ OPERATORS IN CALKIN ALGEBRA
Gopal Datt,NEELIMA OHRI 장전수학회 2018 Proceedings of the Jangjeon mathematical society Vol.21 No.1
We describe some structural properties of a kth-order slant weighted Toeplitz operator Uβκ,Φ(k≥ 2) on L²(β) with Φ∈ L∞(β). The study of this operator and its counterpart on H²(β) is also extended in reference to the Calkin algebra.
NORMALITY CRITERIA FOR A FAMILY OF MEROMORPHIC FUNCTIONS WITH MULTIPLE ZEROS
Datt, Gopal,Li, Yuntong,Rani, Poonam Korean Mathematical Society 2018 대한수학회논문집 Vol.33 No.3
In this article, we prove some normality criteria for a family of meromorphic functions having zeros with some multiplicity. Our main result involves sharing of a holomorphic function by certain differential polynomials. Our results generalize some of the results of Fang and Zalcman [4] and Chen et al. [2] to a great extent.
Weighted composition operators on Lorentz spaces
Subhash Chander Arora,Gopal Datt,Satish Verma 대한수학회 2007 대한수학회보 Vol.44 No.4
In this paper we characterize the boundedness, compactnessand closedness of the range of the weighted composition operators onLorentz spacesL(p;q), 1< p 1 , 1 q 1 .
WEIGHTED COMPOSITION OPERATORS ON LORENTZ SPACES
Arora, Subhash Chander,Datt, Gopal,Verma, Satish Korean Mathematical Society 2007 대한수학회보 Vol.44 No.4
In this paper we characterize the boundedness, compactness and closedness of the range of the weighted composition operators on Lorentz spaces L(p,q), $1<p{\leq}{\infty},\;1{leq}q{leq}{\infty}$.
Ascent and descent of composition operators on Lorentz spaces
Daljeet Singh Bajaj,Gopal Datt 대한수학회 2022 대한수학회논문집 Vol.37 No.1
In this paper, we provide various characterizations for the composition operator on Lorentz spaces $L(p,q)$, $1<p\le \infty$, $1\le q\le\infty$ to have finite ascent (descent) in terms of its inducing measurable transformation. At the end, in order to demonstrate our outcomes, some examples are given.