The thesis is devoted to the study of weak-type, strong-type and maximal estimates for martingale transforms in the weighted context. We put a particular emphasis to the following two aspects of the subject: I. To identify ...

In the following thesis we are studying some consequences of Bednorz-Lata\l{}a theorem concerning the characterization of the Bernoulli process given by the collection $(B_t)_{t\in T}$, where $B_t=\sum_{i\geq1}\varepsilon_i ...

In this thesis we study an application of dynamic programming technique to graph problems and approximation algorithms. We improve upon state-of-the-art algorithms for All-Nodes Shortest Cycles, distance oracles, approximate ...