10 papers
A New Bound for the Gauss Circle Problem
Xi Cen, Xitao Gao, Cheng Zhang +1
Let . We prove that for every , uniformly for real . This breaks the $5…
A sharp regularity threshold for Schrödinger maximal estimates on standard tori
Xi Cen, Xitao Gao, Junyong Zhang
We disprove almost everywhere convergence of the Schrödinger evolution on the standard torus \(\mathbb{T}^d\) for initial data \(f\in H^s(\mathbb{T}^d)\) when \(s<d/(d+2)\), in all…
The discontinuous limit case of an archetypal oscillator with constant excitation and van der Pol damping: A single equilibrium
Xiuli Cen, Hebai Chen, Yilei Tang +1
This paper investigates the global dynamics of the discontinuous limit case of an archetypal oscillator with constant excitation that exhibits a single equilibrium. For parameter r…
The multilinear fractional bounded mean oscillation operator theory I: sparse domination, sparse theorem, off-diagonal extrapolation, quantitative weighted estimate -- for generalized commutators
Xi Cen, Zichen Song
This paper introduces and studies a class of multilinear fractional bounded mean oscillation operators (denoted {\rm -FBMOOs}) defined on ball-basis measure spaces $(X, μ, \math…
The multilinear fractional sparse operator theory II: refining weighted estimates via multilinear fractional sparse forms
Xi Cen
This paper refines the main results from our previous study on sparse bounds of generalized commutators of multilinear fractional singular integral operators in \cite{CenSong2412}.…
The multilinear fractional sparse operator theory I: pointwise domination and weighted estimate
Xi Cen, Zichen Song
How to establish some specific quantitative weighted estimates for the generalized commutator of multilinear fractional singular integral operator is the fo…
New variable weighted conditions for fractional maximal operators over spaces of homogeneous type
Xi Cen
Based on the rapid development of dyadic analysis and the theory of variable weighted function spaces over the spaces of homogeneous type in recent years, we systematical…
Fractional maximal operators on weighted variable Lebesgue spaces over the spaces of homogeneous type
Xi Cen
Let is a space of homogeneous type, we establish a new class of fractional-type variable weights . Then, we get the new weighted strong-type an…
Extrapolation to product Morrey-Herz spaces and applications
Xi Cen, Zichen Song
The purpose of this paper is threefold. First, we introduce product Morrey-Herz spaces and product block-Herz spaces, establish their duality, and prove the boundedness of the stro…
New fractional type weights and the boundedness of some operators
Xi Cen, Qianjun He, Zichen Song +1
Two classes of fractional type variable weights are established in this paper. The first kind of weights are variable multiple weights, which are…