5 papers
An extension of the Wiener-Wintner ergodic theorem for pointwise jointly ergodic systems and its applications
Michihiro Hirayama, Younghwan Son
A joint measure-preserving system is , where each is a measure-preserving system and an…
On the coexistence of divergence and convergence phenomena for the Fourier-Haar series for non-negative functions
Michihiro Hirayama, Davit Karagulyan
Let be the two dimensional Haar system and be the rectangular partial sums of its Fourier series with respect to some $f\in L^1([0,1)^2…
On genericity of non-uniform Dvoretzky coverings of the circle
Michihiro Hirayama, Davit Karagulyan
The classical Dvoretzky covering problem asks for conditions on the sequence of lengths so that the random intervals $I_n : = (ω_n -(\ell_n/2), ω_n +…
Differentiation properties of class with respect to two different basis of rectangles
Michihiro Hirayama, Davit Karagulyan
It is a well-known result by Saks \cite{Saks1934} that there exists a function so that for almost every \[ \lim_{\substack{\mathrm…
On the multiple recurrence properties for disjoint systems
Michihiro Hirayama, Dong Han Kim, Younghwan Son
We consider mutually disjoint family of measure preserving transformations on a probability space . We obtain the multiple recurrence proper…