• SPECTRAL ASYMPTOTICS FOR $\delta$-INTERACTIONS ON SHARP CONES 

  Ourmières-Bonafos T.; Pankrashkin K.; Pizzichillo F. (Journal of Mathematical Analysis and Applications, 2017)

  We investigate the spectrum of three-dimensional Schr\"odinger operators with $\delta$-interactions of constant strength supported on circular cones. As shown in earlier works, such operators have infinitely many eigenvalues ...

• Weighted mixed weak-type inequalities for multilinear operators 

  Li K.; Ombrosi S.; Picardi B. (Studia Mathematica, 2017)

  In this paper we present a theorem that generalizes Sawyer's classic result about mixed weighted inequalities to the multilinear context. Let $\vec{w}=(w_1,...,w_m)$ and $\nu = w_1^\frac{1}{m}...w_m^\frac{1}{m}$, the main ...

• Mixed norm estimates for the Cesàro means associated with Dunkl-Hermite expansions 

  Boggarapu P.; Roncal L.; Thangavelu S. (Transactions of the American Mathematical Society, 2017)

  Our main goal in this article is to study mixed norm estimates for the Cesàro means associated with Dunkl--Hermite expansions on $\mathbb{R}^d$. These expansions arise when one considers the Dunkl--Hermite operator ...

• Dispersive effects of weakly compressible and fast rotating inviscid fluids 

  Ngo V.-S; Scrobogna S. (Discrete and Continuous Dynamical Systems - Series A, 2017-08)

  We consider a system describing the motion of an isentropic, inviscid, weakly compressible, fast rotating fluid in the whole space $\mathbb{R}^3$, with initial data belonging to $ H^s \left( \mathbb{R}^3 \right), s>5/2 $. ...

• On pointwise and weighted estimates for commutators of Calderón-Zygmund operators 

  Lerner A. K; Ombrosi S.; Rivera-Ríos I. P. (Advances in Mathematics, 2017)

  In recent years, it has been well understood that a Calderón-Zygmund operator T is pointwise controlled by a finite number of dyadic operators of a very simple structure (called the sparse operators). We obtain a similar ...

• Weak and strong $A_p$-$A_\infty$ estimates for square functions and related operators 

  Hytönen T.; Li K. (Proceedings of the American Mathematical Society, 2017-07)

  We prove sharp weak and strong type weighted estimates for a class of dyadic operators that includes majorants of both standard singular integrals and square functions. Our main new result is the optimal bound $[w]_{A_p} ...

• The relativistic spherical $\delta$-shell interaction in $\mathbb{R}^3$: spectrum and approximation 

  Mas A.; Pizzichillo F. (Journal of Mathematical Physics, 2017-08-03)

  This note revolves on the free Dirac operator in $\mathbb{R}^3$ and its $\delta$-shell interaction with electrostatic potentials supported on a sphere. On one hand, we characterize the eigenstates of those couplings by ...

• Highly rotating fluids with vertical stratification for periodic data and vanishing vertical viscosity 

  Scrobogna S. (Revista Matemática Iberoamericana, 2017-07)

  We prove that the three-dimensional, periodic primitive equations with zero vertical diffusivity are globally well posed if the Rossby and Froude number are sufficiently small. The initial data is considered to be of zero ...

• Sharp weighted estimates involving one supremum 

  Li K. (Comptes Rendus Mathematique, 2017-07)

  In this note, we study the sharp weighted estimate involving one supremum. In particular, we give a positive answer to an open question raised by Lerner and Moen. We also extend the result to rough homogeneous singular ...

• Derivation of limit equation for a singular perturbation of a 3D periodic Boussinesq system 

  Scrobogna S. (Discrete and Continuous Dynamical Systems - Series A, 2017-07-15)

  We consider a system describing the dynamics of an hydrodynamical, density-dependent flow under the effects of gravitational forces. We prove that if the Froude number is sufficiently small such system is globally well ...

• Monotonicity and convexity of the ratios of the first kind modified Bessel functions and applications 

  Yang Z-H.; Zheng S. (Mathematical Inequalities & Applications, 2017-07-18)

  Let $I_{v}\left( x\right) $ be modified Bessel functions of the first kind. We prove the monotonicity property of the function $x\mapsto I_{u}\left( x\right) I_{v}\left( x\right) /I_{\left( u+v\right) /2}\left( x\right) ...

• Hartree-Fock theory with a self-generated magnetic field 

  Comelli S.; Garcia-Cervera C.J. (Journal of Mathematical Physics, 2017-06-01)

  We prove the existence of a ground state within the Hartree-Fock theory for atoms and molecules, in the presence of self-generated magnetic fields, with and without direct spin coupling. The ground state exists provided ...

• Sharp bounds for the ratio of modified Bessel functions 

  Zheng S.; Yang Z-H. (Mediterranean Journal of Mathematics, 2017-06-21)

  Let $I_{\nu }\left( x\right) $ be the modified Bessel functions of the first kind of order $\nu $, and $S_{p,\nu }\left( x\right) =W_{\nu }\left( x\right) ^{2}-2pW_{\nu }\left( x\right) -x^{2}$ with $W_{\nu }\left( x\right) ...

• Lorentz estimates for asymptotically regular fully nonlinear parabolic equations 

  Zhang J.; Zheng S. (Mathematische Nachrichten, 2017-06-20)

  We prove a global Lorentz estimate of the Hessian of strong solutions to the Cauchy-Dirichlet problem for a class of fully nonlinear parabolic equations with asymptotically regular nonlinearity over a bounded $C^{1,1}$ ...

• Some remarks on the $L^p$ regularity of second derivatives of solutions to non-divergence elliptic equations and the Dini condition 

  Escauriaza L.; Montaner S. (Rendiconti Lincei - Matematica e Applicazioni, 2017-05-30)

  In this note we prove an end-point regularity result on the $L^P$ integrability of the second derivatives of solutions to non-divergence form uniformly elliptic equations whose second derivatives are a priori only known ...

• Gaussian Decay of Harmonic Oscillators and related models 

  Cassano B.; Fanelli L. (Journal of Mathematical Analysis and Applications, 2017-05-15)

  We prove that the decay of the eigenfunctions of harmonic oscillators, uniform electric or magnetic fields is not stable under 0-order complex perturbations, even if bounded, of these Hamiltonians, in the sense that we can ...

• An efficient multigrid strategy for large-scale molecular mechanics optimization 

  Chen J.; García-Cervera C.J. (Journal of Computational Physics, 2017-08-01)

  Static mechanical properties of materials require large-scale nonlinear optimization of the molecular mechanics model under various controls. This paper presents an efficient multigrid strategy to solve such problems. This ...

• A quantitative approach to weighted Carleson condition 

  Rivera-Ríos I.P. (Concrete Operators, 2017-05-05)

  Quantitative versions of weighted estimates obtained by F. Ruiz and J.L. Torrea for the operator \[ \mathcal{M}f(x,t)=\sup_{x\in Q,\,l(Q)\geq t}\frac{1}{|Q|}\int_{Q}|f(x)|dx \qquad x\in\mathbb{R}^{n}, \, t \geq0 \] are ...

• Sparse domination theorem for multilinear singular integral operators with $L^{r}$-Hörmander condition 

  Li K. (Michigan Mathematical Journal, 2017-04-01)

  In this note, we show that if $T$ is a multilinear singular integral operator associated with a kernel satisfies the so-called multilinear $L^{r}$-Hörmander condition, then $T$ can be dominated by multilinear sparse operators.

• A characterization of two weight norm inequality for Littlewood-Paley $g_{\lambda}^{*}$-function 

  Cao M.; Li K.; Xue Q. (Journal of Geometric Analysis, 2017)

  Let $n\ge 2$ and $g_{\lambda}^{*}$ be the well-known high dimensional Littlewood-Paley function which was defined and studied by E. M. Stein, $$g_{\lambda}^{*}(f)(x)=\bigg(\iint_{\mathbb R^{n+1}_{+}} \Big(\frac{t}{t+|x-y ...

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