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Certain multiplier results on Bp spaces

Naik Sunanda

Journal of Applied Analysis

2023

Vol. 29, nr 1

91--98

In this article, we use a particular case of convolution as an operator to discuss a number of problems concerning multiplier results between function spaces such as Hardy and Bp-spaces. As a consequence, we extend certain well-known results on fractional derivatives and fractional integrals. Also, we find condition on the parameters b, c such that Pb,c in Bp.

Adjoint of generalized Cesáro operators on analytic function spaces

Naik Sunanda, Nath Pankaj K.

Journal of Applied Analysis

2020

Vol. 26, nr 2

185--192

In this article, we define a convolution operator and study its boundedness on mixed-norm spaces. In particular,we obtain awell-known result on the boundedness of composition operators given by Avetisyan and Stević in [K. Avetisyan and S. Stević, The generalized Libera transform is bounded on the Besov mixednorm, BMOA and VMOA spaces on the unit disc, Appl. Math. Comput. 213 (2009), no. 2, 304-311]. Also we consider the adjoint Ab,c for b > 0 of two parameter families of Cesáro averaging operators and prove the boundedness on Besov mixed-norm spaces Bp,qα+(c−1) for c > 1.