• $A_1$ theory of weights for rough homogeneous singular integrals and commutators 

  Pérez C.; Rivera-Ríos I.; Roncal L. (Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V, 2019)

  Quantitative $A_1-A_\infty$ estimates for rough homogeneous singular integrals $T_{\Omega}$ and commutators of $\BMO$ symbols and $T_{\Omega}$ are obtained. In particular the following estimates are proved: \[ \|T_\Omega ...

• On the absolute divergence of Fourier series in the infinite dimensional torus 

  Fernández E.; Roncal L. (Colloquium Mathematicum, 2019-03-22)

  In this note we present some simple counterexamples, based on quadratic forms in infinitely many variables, showing that the implication $f\in C^{(\infty}(\mathbb{T}^\omega)\Longrightarrow\sum_{\bar{p}\in\mathbb{Z}^\inf ...

• Hypocoercivity of linear kinetic equations via Harris's Theorem 

  Cañizo J. A.; Cao C.; Evans J.; Yoldaş H. (Kinetic & Related Models, 2019-02-27)

  We study convergence to equilibrium of the linear relaxation Boltzmann (also known as linear BGK) and the linear Boltzmann equations either on the torus $(x,v) \in \mathbb{T}^d \times \mathbb{R}^d$ or on the whole ...

• Improved fractional Poincaré type inequalities in John domains 

  Cejas E.; Drelichman I.; Martínez-Perales J. (Arkiv för Matematik, 2019)

  We obtain improved fractional Poincaré inequalities in John domains of a metric space $(X, d)$ endowed with a doubling measure $\mu$ under some mild regularity conditions on the measure $\mu$. We also give sufficient ...

• Bilinear identities involving the $k$-plane transform and Fourier extension operators 

  Beltran D.; Vega L. (2019)

  We prove certain $L^2(\mathbb{R}^n)$ bilinear estimates for Fourier extension operators associated to spheres and hyperboloids under the action of the $k$-plane transform. As the estimates are $L^2$-based, they follow from ...

• Endpoint Sobolev continuity of the fractional maximal function in higher dimensions 

  Beltran D.; Madrid J. (2019)

  We establish continuity mapping properties of the non-centered fractional maximal operator $M_{\beta}$ in the endpoint input space $W^{1,1}(\mathbb{R}^d)$ for $d \geq 2$ in the cases for which its boundedness is known. ...

• A Hardy-type inequality and some spectral characterizations for the Dirac–Coulomb operator 

  Cassano B.; Pizzichillo F.; Vega L. (Revista Matemática Complutense, 2019-06)

  We prove a sharp Hardy-type inequality for the Dirac operator. We exploit this inequality to obtain spectral properties of the Dirac operator perturbed with Hermitian matrix-valued potentials $\mathbf V$ of Coulomb type: ...

• On extension problem, trace hardy and Hardy’s inequalities for some fractional Laplacians 

  Boggarapu P.; Roncal L.; Thangavelu S. (Communications on pure and applied analysis, 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 ...

• Bloom type upper bounds in the product BMO setting 

  Li K.; Martikainen H.; Vuorinen E. (Journal of Geometric Analysis, 2019-04-08)

  We prove some Bloom type estimates in the product BMO setting. More specifically, for a bounded singular integral $T_n$ in $\mathbb R^n$ and a bounded singular integral $T_m$ in $\mathbb R^m$ we prove that $$ \| [T_n^1, ...

• Convex Integration Arising in the Modelling of Shape-Memory Alloys: Some Remarks on Rigidity, Flexibility and Some Numerical Implementations 

  Rüland, A.; Taylor J. M.; Zillinger, C. (Journal of Nonlinear Science, 2019-03-30)

  We study convex integration solutions in the context of the modelling of shape-memory alloys. The purpose of the article is twofold, treating both rigidity and flexibility prop- erties: Firstly, we relate the maximal ...

• Topological singular set of vector-valued maps, I: application to manifold-constrained Sobolev and BV spaces 

  Canevari G.; Orlandi G. (Calculus of Variations and Partial Differential Equations, 2019-03-30)

  We introduce an operator $\mathbf{S}$ on vector-valued maps $u$ which has the ability to capture the relevant topological information carried by $u$. In particular, this operator is defined on maps that take values in a ...

• Order Reconstruction for neatics on squares with isotropic inclusions: A Landau-de Gennes study 

  Wang Y.; Canevari G.; Majumdar A. (SIAM Journal on Applied Mathematics, 2019-03-30)

  e study a modified Landau-de Gennes model for nematic liq- uid crystals, where the elastic term is assumed to be of subquadratic growth in the gradient. We analyze the behaviour of global minimizers in two- and three-dimensional ...

• Bloom type inequality for bi-parameter singular integrals: efficient proof and iterated commutators 

  Li K.; Martikainen H.; Vuorinen E. (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 $T$ ...

• Boundary Triples for the Dirac Operator with Coulomb-Type Spherically Symmetric Perturbations 

  Cassano B.; Pizzichillo F. (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 

  Di Plinio F.; Hytönen T.; Li K. (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, ...

• The excluded volume of two-dimensional convex bodies: shape reconstruction and non-uniqueness 

  Taylor J. M. (Journal of Physics A: Mathematical and Theoretical, 2019-02-05)

  In the Onsager model of one-component hard-particle systems, the entire phase behaviour is dictated by a function of relative orientation, which represents the amount of space excluded to one particle by another at this ...

• Asymptotic models for free boundary flow in porous media 

  Granero-Belinchón R.; Scrobogna S. (Physica D, 2019)

  We provide rigorous asymptotic models for the free boundary Darcy and Forchheimer problem under the assumption of weak nonlinear interaction, in a regime in which the steepness parameter of the interface is considered to ...

• On the influence of gravity on density-dependent incompressible periodic fluids 

  Ngo V.-S.; Scrobogna S. (J. Differential Equations, 2019)

  The present work is devoted to the analysis of density-dependent, incompressible fluids in a 3D torus, when the Froude number $\varepsilon$ goes to zero. We consider the very general case where the initial data do not have ...

• Unique determination of the electric potential in the presence of a fixed magnetic potential in the plane 

  Caro P.; Rogers K. (2018-12)

  For electric and magnetic potentials with compact support, we consider the magnetic Schrödinger equation with fixed positive energy. Under a mild additional regularity hypothesis, and with fixed magnetic potential, we show ...

• Determination of convection terms and quasi-linearities appearing in diffusion equations 

  Caro P.; Kian Y. (2018-12)

  We consider the highly nonlinear and ill posed inverse problem of determining some general expression appearing in the a diffusion equation from measurements of solutions on the lateral boundary. We consider both linear ...

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