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Bloom type inequality for bi-parameter singular integrals: efficient proof and iterated commutators
(International Mathematics Research Notices, 2019-03-14)Utilising some recent ideas from our bilinear bi-parameter theory, we give an efficient proof of a two-weight Bloom type inequality for iterated commutators of linear bi-parameter singular integrals. We prove that if $T$ ... -
Fractional kinetics in random/complex media
(Handbook of Fractional Calculus with Applications Volume 5 Applications in Physics, Part B, 2019)In this chapter, we consider a randomly-scaled Gaussian process and discuss a number of applications to model fractional diffusion. Actually, this approach can be understood as a Gaussian diffusion in a medium characterized ... -
Fractional Brownian motion in a finite interval: correlations effect depletion or accretion zones of particles near boundaries
(New Journal of Physics, 2019-02)Fractional Brownian motion (FBM) is a Gaussian stochastic process with stationary, long-time correlated increments and is frequently used to model anomalous diffusion processes. We study numerically FBM confined to a finite ... -
Boundary Triples for the Dirac Operator with Coulomb-Type Spherically Symmetric Perturbations
(Journal of Mathematical Physics, 2019-02)We determine explicitly a boundary triple for the Dirac operator $H:=-i\alpha\cdot \nabla + m\beta + \mathbb V(x)$ in $\mathbb R^3$, for $m\in\mathbb R$ and $\mathbb V(x)= |x|^{-1} ( \nu \mathbb{I}_4 +\mu \beta -i \lambda ... -
Sparse bounds for maximal rough singular integrals via the Fourier transform
(Annales de l'institut Fourier, 2019-03-12)We prove a quantified sparse bound for the maximal truncations of convolution-type singular integrals with suitable Fourier decay of the kernel. Our result extends the sparse domination principle by Conde-Alonso, Culiuc, ...
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