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Parasar Mohanty

Publications and source records attributed to Parasar Mohanty.

8 recordsLinked to original sources
arXiv2022

Equality in Hausdorff-Young for Hypergroups

It has been shown in "On the Hausdorff-Young theorem for commutative hypergroups" by Sina Degenfeld-Schonburg, that one can extend the domain of Fourier transform of a commutative hypergroup $K$ to $L^p(K)$ for $1\leq p \leq 2$, and the Hausdorff-Young inequality holds true for these cases. In this article, we examine the structure of non-zero functions in $L^p(K)$ for which equality is attained in the Hausdorff-Young inequality, for $1<p<2$, and further provide a characterization for the basic uncertainty principle for commutative hypergroups with non-trivial centre.

math.FA↗
arXiv2021

Weak type bounds for rough maximal singular integrals near $L^1$

In this paper it is shown that for $Ω\in L\log L(\mathbb{S}^{d-1})$, the rough maximal singular integral operator $T_Ω^*$ is of weak type $L\log\log L(\mathbb{R}^d)$. Furthermore, for $w\in A_1$ and $Ω\in L^\infty(\mathbb{S}^{d-1})$, it is shown that $T_Ω^*$ is of weak type $L\log\log L(w)$ with weight dependence $[w]_{A_1}[w]_{A_{\infty}}\log([w]_{A_{\infty}}+1),$ which is same as the best known constant for the singular integral $T_Ω$.

math.CA↗
arXiv2020

On Joint Functional Calculus For Ritt Operators

In this paper, we study joint functional calculus for commuting $n$-tuple of Ritt operators. We provide an equivalent characterisation of boundedness for joint functional calculus for Ritt operators on $L^p$-spaces, $1< p<\infty$. We also investigate joint similarity problem and joint bounded functional calculus on non-commutative $L^p$-spaces for $n$-tuple of Ritt operators. We get our results by proving a suitable multivariable transfer principle between sectorial and Ritt operators as well as an appropriate joint dilation result in a general setting.

math.CA↗
arXiv2019

A non-abelian, non-Sidon, completely bounded $Λ(p)$ set

The purpose of this note is to construct an example of a discrete non-abelian group $G$ and a subset $E$ of $G$, not contained in any abelian subgroup, that is a completely bounded $Λ(p)$ set for all $p<\infty ,$ but is neither a Leinert set nor a weak Sidon set.

math.FA↗
arXiv2012

Fourier Multipliers and Littlewood-Paley For Modulation Spaces

In this paper we have studied Fourier multipliers and Littlewood-Paley square functions in the context of modulation spaces. We have also proved that any bounded linear operator from modulation space $\mathcal{M}_{p,q}(\R^n), 1\leq p,q\leq \infty,$ into itself possesses an $l_2-$valued extension. This is an analogue of a well known result due to Marcinkiewicz and Zygmund on classical $L^p-$spaces.

math.CA↗
arXiv2003

A product convergence theorem for Henstock--Kurzweil integrals

Necessary and sufficient for $\int_a^bfg_n\to \int_a^bfg$ for all Henstock--Kurzweil integrable functions $f$ is that $g$ be of bounded variation, $g_n$ be uniformly bounded and of uniform bounded variation and, on each compact interval in $(a,b)$, $g_n\to g$ in measure or in the $L^1$ norm. The same conditions are necessary and sufficient for $\|f(g_n-g)\|\to 0$ for all Henstock--Kurzweil integrable functions $f$. If $g_n\to g$ a.e. then convergence $\|fg_n\|\to\|fg\|$ for all Henstock--Kurzweil integrable functions $f$ is equivalent to $\|f(g_n-g)\|\to 0$. This extends a theorem due to Lee Peng-Yee.

math.CA↗