Anoop V P

Anoop V. P. is an active researcher in modern analysis, particularly in the field of Harmonic Analysis and its interaction with special function theory and partial differential equations. His work is centered on extending and refining classical functional inequalities to more general and structurally rich settings, especially those involving Dunkl operators — a class of differential-difference operators associated with reflection groups that generalize standard Laplacian-based analysis. A significant portion of his research has been devoted to studying Hardy-type and Sobolev-type inequalities in the Dunkl setting. In collaboration with Sanjay Parui and others, he has developed improved versions of fractional Hardy inequalities, examined trace inequalities, and analyzed extremals for Sobolev-type embeddings involving Dunkl gradients and potentials. His work on the Hardy inequality and its fractional counterparts for the Dunkl Laplacian has contributed to a deeper understanding of how classical analytic inequalities adapt to non-Euclidean symmetries. In addition, Anoop has explored variants of the Hardy–Littlewood–Sobolev inequality, including formulations in upper half-space domains and in the context of Dunkl-type Riesz potentials. His joint work with Saswata Adhikari and Sanjay Parui established existence results for extremals in these generalized settings, which are important for understanding sharp constants and optimal functions in inequality theory. His publications have appeared in respected international journals such as Israel Journal of Mathematics, Mathematical Inequalities & Applications, Complex Analysis and Operator Theory, Collectanea Mathematica, and Annales Mathématiques Blaise Pascal. Across these works, Anoop’s research consistently advances the study of functional inequalities by blending classical harmonic analysis with the algebraic structure of reflection groups. Overall, his contributions lie in pushing the boundaries of inequality theory into new analytical frameworks, offering both refined estimates and structural insights that are relevant to researchers in harmonic analysis, special functions, and partial differential equations.