5 citations · 9 across the 13 of their papers we have counts for
11 papers · 1 filter
On the diameter of the stopped spider process
Ewelina Bednarz, Philip A. Ernst, Adam Osekowski
We consider the Brownian ``spider process'', also known as Walsh Brownian motion, first introduced in the epilogue of Walsh 1978. The paper provides the best constant for the…
A dual approach to Burkholder's estimates
Rodrigo Bañuelos, Tomasz Gałązka, Adam Osękowski
The paper contains an alternative proof of the celebrated estimates for differentially subordinate martingales established by Burkholder and Wang in the eighties and nineties…
Burkholder's function and a weighted bound for stochastic integrals
Rodrigo Banuelos, Michal Brzozowski, Adam Osekowski
Let be a continuous-path martingale and let be a stochastic integral, with respect to , of some predictable process with values in . We provide an explicit formu…
Weighted square function estimates
Rodrigo Banuelos, Adam Osekowski
The paper contains the proof of -weighted norm inequalities for both, martingales square functions and the classical square functions in harmonic analysis of Littlewood-Paley…
Stability in Burkholder's differentially subordinate martingales inequalities and applications to Fourier multipliers
Rodrigo Banuelos, Adam Osekowski
We study stability estimates for the almost extremal functions associated with the -bound for the real and imaginary parts of the Beurling-Ahlfors operator. The proof exploits…
On the Bellman function of Nazarov, Treil and Volberg
Rodrigo Banuelos, Adam Osekowski
We give an explicit formula for the Bellman function associated with the dual bound related to the unconditional constant of the Haar system.
Sharp maximal -estimates for martingales
Rodrigo Bañuelos, Adam Osekowski
Let be a supermartingale starting from which has only nonnegative jumps. For each we determine the best constants , and such that $$ \,\…
On Astala's theorem for martingales and Fourier multipliers
Rodrigo Banuelos, Adam Osekowski
We exhibit a large class of symbols on , , for which the corresponding Fourier multipliers satisfy the following inequality. If , are measurable sub…
Sharp martingale inequalities and applications to Riesz transforms on manifolds, Lie groups and Gauss space
Rodrigo Banuelos, Adam Osekowski
We prove new sharp , logarithmic, and weak-type inequalities for martingales under the assumption of differentially subordination. The estimates are "Fyenman-Kac" type v…
Burkholder inequalities for submartingales, Bessel processes and conformal martingales
Rodrigo Bañuelos, Adam Osȩkowsk
The motivation for this paper comes from the following question on comparison of norms of conformal martingales , in , . Suppose that is differentially su…
Martingales and Sharp Bounds for Fourier multipliers
Rodrigo Bañuelos, Adam Oȩkowski
Using the argument of Geiss, Montgomery-Smith and Saksman \cite{GMSS}, and a new martingale inequality, the --norms of certain Fourier multipliers in , , are id…