Variational estimate for the family of discrete averages associated to simplices
We prove $\ell^2(\mathbb{Z}^n)-$estimate of long $r$-variational seminorm for the family of discrete averages associated to simplices.
math.NT↗
arXiv subjects
Siddhartha Samanta
Publications and source records attributed to Siddhartha Samanta.
$\ell^p(\mathbb{Z}^n)$-estimate for long $r$-variational seminorm of discrete Birch-Magyar averages
We prove $\ell^p(\mathbb{Z}^n)-$estimates for long $r$-variational seminorm of two families of averages: discrete Birch-Magyar averages, for $r>max\{p,p'\}$ with $p>\frac{2c_{\mathfrak{R}}-2}{2c_{\mathfrak{R}}-3}$ and discrete Hardy-Littlewood type averages over certain algebraic varieties, for $r>max\{p,p'\}$ with $p>1$. Further, we discuss an application of these results in ergodic theory.
math.NT↗
Sparse Bounds for Discrete Maximal Functions associated with Birch-Magyar averages
In this article, we study discrete maximal function associated with the Birch-Magyar averages over sparse sequences. We establish sparse domination principle for such operators. As a consequence, we obtain $\ell^p$-estimates for such discrete maximal function over sparse sequences for all $p>1$. The proof of sparse bounds is based on scale-free $\ell^p-$improving estimates for the single scale Birch-Magyar averages.
math.NT↗