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Manasa N. Vempati

Publications and source records attributed to Manasa N. Vempati.

14 recordsLinked to original sources
arXiv2026

Bilinear Bochner-Riesz Means on the Complex Sphere

In this paper, we establish the boundedness of the bilinear Bochner-Riesz means $\mathcal{B}^α_R$ on the complex sphere $\mathbb{S}$. More precisely, we prove that $\mathcal{B}^α_R$ is bounded from $L^{p_1}(\mathbb{S}) \times L^{p_2}(\mathbb{S}) \to L^p(\mathbb{S})$ where $1/p_1+1/p_2=1/p$ and $1\leq p_1, p_2 \leq \infty$, for an admissible range of exponents, with the required smoothness parameter $α$ described in terms of the topological dimension of $\mathbb{S}$. To facilitate our proof, we establish several analytic estimates, including restriction-type estimates, weighted Plancherel estimates with large power of weights and bilinear weighted Plancherel estimates, which are derived from the ground up in our setting and may be considered of independent interest.

math.CA↗
arXiv2026

Sparse Operators and their boundedness on Morrey-type Spaces: An Expository Note

Sparse domination is a central tool in modern harmonic analysis, offering a unified approach to weighted inequalities for Calderón--Zygmund operators and related operators such as commutator operators, rough singular integrals, square functions etc. In this expository note, we briefly survey the main ideas behind sparse bounds on $L^p$ and weighted $L^p$ spaces, and discuss boundedness results for sparse operators on Morrey and generalized Morrey spaces. We establish a model result on the boundedness of sparse operators on Komori--Shirai type weighted Morrey spaces $L^{p,κ}(w)$, $w\in A_p$. These bounds offer a simpler framework for deriving Morrey-space estimates for Calderón--Zygmund operators and related operators via sparse domination. We conclude with remarks about extensions and connections to other Morrey space settings.

math.FA↗
arXiv2026

On Schrödinger Pseudo-Multipliers and their Commutators

In this article, we establish the unweighted and weighted $L^p$-boundedness of pseudo-multipliers associated with a class of Schrödinger operators, this generalizes the result of our first author and Thangavelu [Bagchi \& Thangavelu, J. Funct. Anal. 2015] for Hermite pseudo-multipliers. The weight classes we consider are tailored to this framework and strictly contain the classical Muckenhoupt $A_p$-classes. To establish the weighted boundedness, we prove a quantitative version of reverse Hölder's inequality and quantitative weighted estimates for general sparse operators, which are of independent interest. We also study commutators of Schrödinger pseudo-multipliers, establishing their boundedness and compactness results on these weighted $L^p$-spaces.

math.AP↗
arXiv2025

Compactness of the Bloom sparse operators and applications

We establish the characterization of compactness for the sparse operator (associated with symbol in weighted VMO space) in the two weight setting on the spaces of homogeneous type in the sense of Coifman and Weiss. As a direct application we obtain the compactness characterization for the maximal commutators with respect to the weighted VMO functions and the commutator of Calderón-Zygmund operators on the homogeneous spaces. Furthermore, our approach can be applied to compactness characterization for operators in the multilinear Bloom setting.

math.CA↗
arXiv2024

Commutators of Maximal Operators on Weighted Morrey Spaces

In this article we obtain the characterization for the commutators of maximal functions on the weighted Morrey spaces in the setting of spaces of homogeneous type. More precisely, we characterize BMO spaces using the commutators of Hardy-Littlewood maximal function, sharp and fractional maximal functions.

math.FA↗
arXiv2024

A Density Theorem for Higher Order Sums of Prime Numbers

Let $P$ be a subset of the primes of lower density strictly larger than $\frac12$. Then, every sufficiently large even integer is a sum of four primes from the set $P$. We establish similar results for $k$-summands, with $k\geq 4$, and for $k \geq 4$ distinct subsets of primes. This extends the work of H.~Li, H.~Pan, as well as X.~Shao on sums of three primes, and A.~Alsteri and X.~Shao on sums of two primes. The primary new contributions come from elementary combinatorial lemmas.

math.NT↗
arXiv2021

A metric approach to sparse domination

We present a general approach to sparse domination based on single-scale $L^p$-improving as a key property. The results are formulated in the setting of metric spaces of homogeneous type and avoid completely the use of dyadic-probabilistic techniques as well as of Christ-Hytönen-Kairema cubes. Among the applications of our general principle, we recover sparse domination of Dini-continuous Calderón-Zygmund kernels on spaces of homogeneous type, we prove a family of sparse bounds for maximal functions associated to convolutions with measures exhibiting Fourier decay, and we deduce sparse estimates for Radon transforms along polynomial submanifolds of $\mathbb R^n$.

math.CA↗
arXiv2020

A note on two weight commutators of maximal functions on spaces of homogeneous type

We study the two weight quantitative estimates for the commutator of maximal functions and the maximal commutators with respect to the symbol in weighted BMO space on spaces of homogeneous type. These commutators turn out to be controlled by the sparse operators in the setting of space of homogeneous type. The lower bound of the maximal commutator is also obtained.

math.FA↗
arXiv2020

A note on commutators on weighted Morrey spaces on spaces of homogeneous type

In this paper we study the boundedness and compactness characterizations of the commutator of Calderón-Zygmund operators $T$ on spaces of homogeneous type $(X,d,μ)$ in the sense of Coifman and Weiss. More precisely, We show that the commutator $[b, T]$ is bounded on weighted Morrey space $L_ω^{p,κ}(X)$ ($κ\in(0,1), ω\in A_{p}(X), 1<p<\infty$) if and only if $b$ is in the BMO space. Moreover, the commutator $[b, T]$ is compact on weighted Morrey space $L_ω^{p,κ}(X)$ ($κ\in(0,1), ω\in A_{p}(X), 1<p<\infty$) if and only if $b$ is in the VMO space.

math.CA↗
arXiv2020

Boundedness And Compactness Of Cauchy-Type Integral Commutator On Weighted Morrey Spaces

In this paper we study the boundedness and compactness characterizations of the commutator of Cauchy type integrals $\mathcal C$ on a bounded strongly pseudoconvex domain $D$ in $C^n$ with boundary $bD$ satisfying the minimum regularity condition $C^{2}$ based on the recent result of Lanzani-Stein and Duong-Lacey-Li-Wick-Wu. We point out that in this setting the Cauchy type integral $\mathcal C$ is the sum of the essential part $\mathcal{C}^\sharp$ which is a Calderón-Zygmund operator and a remainder $\mathcal R$ which is no longer a Calderón-Zygmund operator. We show that the commutator $[b, \mathcal C]$ is bounded on weighted Morrey space $L_{v}^{p,κ}(bD)$ ($v\in A_p, 1<p<\infty$) if and only if $b$ is in the BMO space on $bD$. Moreover, the commutator $[b, \mathcal C]$ is compact on weighted Morrey space $L_{v}^{p,κ}(bD)$ ($v\in A_p, 1<p<\infty$) if and only if $b$ is in the VMO space on $bD$.

math.CV↗
arXiv2020

A two weight inequality for Calderón-Zygmund operators on spaces of homogeneous type with applications

Let $(X,d,μ)$ be a space of homogeneous type in the sense of Coifman and Weiss, i.e. $d$ is a quasi metric on $X$ and $μ$ is a positive measure satisfying the doubling condition. Suppose that $u$ and $v$ are two locally finite positive Borel measures on $(X,d,μ)$. Subject to the pair of weights satisfying a side condition, we characterize the boundedness of a Calderón--Zygmund operator $T$ from $L^{2}(u)$ to $L^{2}(v)$ in terms of the $A_{2}$ condition and two testing conditions. For every cube $B\subset X$, we have the following testing conditions, with $\mathbf{1}_{B}$ taken as the indicator of $B$ \begin{equation*} \Vert T(u\mathbf{1}_{B})\Vert _{L^{2}(B, v)}\leq \mathcal{T}\Vert 1_{B}\Vert _{L^{2}(u)}, \end{equation*} \begin{equation*} \Vert T^{\ast }(v\mathbf{1}_{B})\Vert _{L^{2}(B, u)}\leq \mathcal{T}\Vert 1_{B}\Vert _{L^{2}(v)}. \end{equation*} The proof uses stopping cubes and corona decompositions originating in work of Nazarov, Treil and Volberg, along with the pivotal side condition.

math.CA↗