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Quantitative weighted estimates for Rubio de Francia's Littlewood--Paley square function
(2019-12)
We consider the Rubio de Francia's Littlewood--Paley square function associated with an arbitrary family of intervals in $\mathbb{R}$ with finite overlapping.
Quantitative weighted estimates are obtained for this operator. ...
Bilinear identities involving the k-plane transform and Fourier extension operators
(2019-11-30)
We prove certain L2pRnq bilinear estimates for Fourier extension operators associ- ated to spheres and hyperboloids under the action of the k-plane transform. As the estimates are L2-based, they follow from bilinear ...
Some geometric properties of Riemann’s non-differentiable function
(2019-11-06)
Riemann’s non-differentiable function is a celebrated example of a continuous but almost nowhere differentiable function. There is strong numeric evidence that one of its complex versions represents a geometric trajectory ...
Flow with $A_\infty(\mathbb R)$ density and transport equation in $\mathrm{BMO}(\mathbb R)$
(2019-11)
We show that, if $b\in L^1(0,T;L^1_{\rm {loc}}(\mathbb R))$ has
spatial derivative in the John-Nirenberg space ${\rm{BMO}}(\mathbb R)$, then it generates a unique flow $\phi(t,\cdot)$ which has an $A_\infty(\mathbb R)$ ...
Análisis de Fourier en el toro infinito-dimensional
(2019-10-24)
Se presentan algunos resultados originales de análisis armónico para funciones definidas en el toro infinito, que es el grupo topológico compacto consistente en el producto cartesiano de una familia numerable de toros ...
Bilinear Calderón--Zygmund theory on product spaces
(2019-10)
We develop a wide general theory of bilinear bi-parameter singular integrals $T$. This includes general Calder\'on--Zygmund type principles in the bilinear bi-parameter setting:
easier bounds, like estimates in the Banach ...
Carleman type inequalities for fractional relativistic operators
(2019-09-22)
In this paper, we derive Carleman estimates for the fractional relativistic operator. Firstly, we consider changing-sign solutions to the heat equation for such operators. We prove monotonicity inequalities and convexity ...
On the Evolution of the Vortex Filament Equation for regular M-polygons with nonzero torsion
(2019-09-03)
In this paper, we consider the evolution of the Vortex Filament equa- tion (VFE):
Xt = Xs ∧ Xss,
taking M-sided regular polygons with nonzero torsion as initial data. Us- ing algebraic techniques, backed by numerical ...
On extension problem, trace hardy and Hardy’s inequalities for some fractional Laplacians
(2019-09)
We obtain generalised trace Hardy inequalities for fractional powers of general operators given by sums of squares of vector fields. Such inequalities are derived by means of particular solutions of an extended equation ...
Asymptotic behaviour of some nonlocal equations in mathematical biology and kinetic theory
(2019-09)
We study the long-time behaviour of solutions to some partial differential equations arising in modeling of several biological and physical phenomena. In this work, the type of the equations we consider is mainly nonlocal, ...