- Harmonic Analysis : We study the discrete version of a class of operators such as Hardy-Littlewood maximal operator, Singular Integral operators on variable Lebesgue spaces and their ergodic version. We use the methodologies Calderon-Zygmund decomposition, Calderon - Coifman - Weiss transference principle and Interpolation theorem which are valid in variable Lebesgue spaces also. We have obtained certain results in the discretized version of Hardy-Littlewood maximal operator in variable Lebesgue spaces.
- Graph Theory : We study the problem of Domination on Graphs. Our main focus is to address the NP completeness of this problems by adopting the following two ways : 1. Studying this problem on some specific class of graphs, and 2. by using kernelization technique
PhD Students:
1. Name : A. Sri Sakti Swarup
Title : A Class of operators on variable exponent sequence spaces and their corresponding ergodic version.
My Role : Guide
Status : Achieved results on boundedness of Discrete Maximal Operators and Discrete Singular integrals on Variable Exponent Spaces. One paper is communicated to Journal of Mathematical Inequalities and Applications. Another papers on Singular Integrals is under preparation.
2. Name : Tusharakanta Pradhan
Title : Studies on Pseudo - Differential Operators and their applications
My Role : Co-Guide
Status : Completed