In this thesis we deal with two problems in harmonic analysis. In the first problem we discuss weighted norm inequalities for Weyl multipliers satisfying Mauceri’s condition. As an application, we prove certain multiplier ...

We deal with two themes that are illustrative of the rigidity and regularity of holomorphic mappings. The first one concerns the regularity of continuous CR mappings between smooth pseudo convex, finite type hypersurfaces ...

Consider (1) -yn1+ q1y1 = (λr11 + µr12)y1 on [0, 1] y’1(0) = cot α1 and = y’1(1) = a1λ + b1 y1(0) y1(1) ...

We characterise the higher order Riesz transforms on the Heisenberg group and also show that they satisfy dimension-free bounds under some assumptions on the multipliers. We also prove the boundedness of the higher order ...

Cytotoxic T-lymphocytes (CTLs) are important components of the adaptive immune system and function by scanning the intracellular environment so as to detect and de-stroy infected cells. CTL responses play a major role in ...

The main emphasis of this thesis is to study a posteriori error analysis of discontinuous Galerkin (DG) methods for the elliptic variational inequalities. The DG methods have become very pop-ular in the last two decades ...

In this thesis we investigate single and multi-player stochastic dynamic optimization prob-lems. We consider both discrete and continuous time processes. In the multi-player setup we investigate zero-sum games with both ...

Gromov’s compactness theorem for metric spaces, a compactness theorem for the space of compact metric spaces equipped with the Gromov-Hausdorff distance, is a theorem with many applications. In this thesis, we give a ...

In this thesis we present a formalization of the combinatorial part of the proof of Feit-Higman theorem on generalized polygons. Generalised polygons are abstract geometric structures that generalize ordinary polygons and ...