Related papers: Derivative Formula and Gradient Estimates for Grus…

This is a continuation of our work [BBGG23, BBGG22] where we have initiated the study of sparse domination and quantitative weighted estimates for Grushin pseudo-multipliers. In this article, we further extend this analysis to study…

Given $\Omega(\subseteq\;R^{1+m})$, a smooth bounded domain and a nonnegative measurable function $f$ defined on $\Omega$ with suitable summability. In this paper, we will study the existence and regularity of solutions to the quasilinear…

Let $\Delta_\kappa$ be the Dunkl Laplacian on $\mathbb{R}^n$ and $\phi: \mathbb{R}^+ \to \mathbb{R}$ is a smooth function. The aim of this manuscript is twofold. First, we study the decay estimate for a class of dispersive semigroup of the…

We establish a Harnack inequality for a class of quasi-linear PDE modeled on the prototype {equation*} \partial_tu= -\sum_{i=1}^{m}X_i^\ast (|\X u|^{p-2} X_i u){equation*} where $p\ge 2$, $ \ \X = (X_1,..., X_m)$ is a system of Lipschitz…

Let $G$ be a $\mathbb{Q}_p$-split reductive group with connected centre and Borel subgroup $B=TN$. We construct a right exact functor $D^\vee_\Delta$ from the category of smooth modulo $p^n$ representations of $B$ to the category of…

The Deligne-Simpson problem (DSP) (resp. the weak DSP) is formulated like this: {\em give necessary and sufficient conditions for the choice of the conjugacy classes $C_j\subset GL(n,{\bf C})$ or $c_j\subset gl(n,{\bf C})$ so that there…

Let (P(t)) be the Ornstein-Uhlenbeck semigroup associated with the stochastic Cauchy problem dU(t) = AU(t)dt + dW_H(t), where A is the generator of a C_0-semigroup (S(t)) on a Banach space E, H is a Hilbert subspace of E, and (W_H(t)) is an…

A formula is given for the profinite genus of groups of the form $\mathbb{Z}^n \rtimes C_{p^2}$, completing the calculation of the size of the genus of semidirect products of the form $\mathbb{Z}^n \rtimes G$ where $G$ is a finite $p$-group…

In this paper, we derive new estimates for the remainder term of the midpoint, trapezoid, and Simpson formulae for functions whose derivatives in absolute value at certain power are P-functions. Some applications to special means of real…

We present a local weighted estimate for the Riesz potential in $\mathbb{R}^n$, which improves the main theorem of Alberico, Cianchi, and Sbordone [C. R. Math. Acad. Sci. Paris \textbf{347} (2009)] in several ways. As a consequence, we…

Gaussian processes (GPs) with derivatives are useful in many applications, including Bayesian optimization, implicit surface reconstruction, and terrain reconstruction. Fitting a GP to function values and derivatives at $n$ points in $d$…

The \textit{method of semigroups} is a unifying, widely applicable, general technique to formulate and analyze fundamental aspects of fractional powers of operators $L$ and their regularity properties in related functional spaces. The…

In this article we prove some Lipschitz estimates and existence result for a class of degenerate fully nonlinear elliptic equations which are a generalization of the pseudo p-Laplacian. The operators are degenerate elliptic at any point…

In this paper, we investigate dispersive estimates for the time evolution of Hamiltonians $$ H=-\Delta+\sum_{j=1}^N\langle\cdot\,, \varphi_j\rangle \varphi_j\quad\,\,\,\text{in}\,\,\,\mathbb{R}^d,\,\, d\ge 1, $$ where each $\varphi_j$…

In this paper, we consider a class of reflected stochastic differential equations for which the constraint is not on the paths of the solution but on its law. We establish a small noise large deviation principle, a large deviation for short…

By using absolutely continuous lower bounds of the L\'evy measure, explicit gradient estimates are derived for the semigroup of the corresponding L\'evy process with a linear drift. A derivative formula is presented for the conditional…

The Garside group, as a generalization of braid groups and Artin groups of finite types, is defined as the group of fractions of a Garside monoid. We show that the semidirect product of Garside monoids is a Garside monoid. We use the…

We establish the existence of nontrivial nonnegative weak solutions to the following equation \begin{equation*} -\Delta_\gamma u + V(z)u = Q(z)f(u), \quad z\in \mathbb{R}^N, \end{equation*} where $\Delta_\gamma $ denotes the so-called…

Unique existence of analytically strong solutions to stochastic partial differential equations (SPDE) with drift given by the subdifferential of a quasi-convex function and with general multiplicative noise is proven. The proof applies a…

In this paper, we first derive some explicit formulas for the computation of the n-th order divergence operator in Malliavin calculus in the one-dimensional case. We then extend these results to the case of isonormal Gaussian space. Our…