Related papers: The Douglas formula in $L^p$

We prove denominator identities for the periplectic Lie superalgebra $\mathfrak{p}(n)$, thereby completing the problem of finding denominator identities for all simple classical finite-dimensional Lie superalgebras.

We provide a simple and direct proof of a strong-type unique continuation principle for the fractional $p$-Laplacian $(-\Delta_p)^s$ for a range of $s$ and $p$. The result extends to strong solutions of the fractional nonlinear…

We prove a transformation formula relating two determinants involving elliptic shifted factorials. Similar determinants have been applied to multiple elliptic hypergeometric series.

The goal of this note is to give, at least for a restricted range of indices, a short proof of homogeneous commutator estimates for fractional derivatives of a product, using classical tools. Both $L^{p}$ and weighted $L^{p}$ estimates can…

We show there exists an L^p solution, for p>2, to the dbar-Neumann problem on an edge domain in C^2 for (0,1)-forms, and we explicitly compute the singularities, which are of complex logarithmic and arctangent type, along the edge, of the…

By using duality, it is shown that there exist near-minimizers for the distance functionals for the couple $(L^\infty, L^p)$, $1<p<\infty$, that are stable under the action of singular integral operators.

We prove $L^{p}$-boundedness of oscillating multipliers on all symmetric spaces and a class of locally symmetric spaces.

Suppose $p$ is a computable real so that $p \geq 1$. We show that in both the real and complex case $l^p$ is computably categorical if and only if $p \neq 2$.

We study the distribution of values of automorphic $L$-functions in a family of holomorphic cusp forms with prime level. We prove an asymptotic formula for a certain density function closely related to this value-distribution. The formula…

We prove L^1 --> L^\infty estimates for the linear Schroedinger equation in three dimensions. The potential is assumed to belong to certain L^p spaces, but no pointwise decay estimates and no additional regularity is required.

We give a direct proof of the operator valued Hardy-Littlewood maximal inequality for $2<p<\infty$.

Consider the Landau equation with Coulomb potential in a periodic box. We develop a new $L^{2}\rightarrow L^{\infty }$ framework to construct global unique solutions near Maxwellian with small $L^{\infty }\ $norm. The first step is to…

We consider a class of nonautonomous parabolic first-order coupled systems in the Lebesgue space $L^p({\mathbb R}^d;{\mathbb R}^m)$, $(d,m \ge 1)$ with $p\in [1,+\infty)$. Sufficient conditions for the associated evolution operator ${\bf…

We study the $l_p$ Hausdorff distance from convex hull of a compact set $A\subset\mathbb{R}^n$, which is the distance \begin{equation*} d^{(l_p)}(A):=\sup_{x\in conv(A)}\inf_{a\in A}\|x-a\|_p, \end{equation*} where $\|\cdot\|_p$ is the…

Inspired by the work of Cossetti and D'Arca [CD25], we show that the general weighted $L^{p}$-Hardy type inequalities [CD25, Theorems 1.1 and 1.2] and the corresponding identities hold for all $1<p<\infty$, thus extending their results…

In this note we consider a tent-like family with a cusp at the singular point and show that the linear response holds for certain perturbations of this family. This contrasts the tent-like maps with finite derivatives at the singularity.…

We use GL(2) delta method to establish the Burgess bound.

We give necessary and sufficient conditions for the existence of weak solutions to the model equation $$-\Delta_p u=\sigma \, u^q \quad \text{on} \, \, \, \R^n,$$ in the case $0<q<p-1$, where $\sigma\ge 0$ is an arbitrary locally integrable…

We compute the numerical index of the two-dimensional real $L_p$ space for $\frac65\leq p\leq \frac32$ and $3\leq p\leq 6$.

We prove a Hopf's lemma in the point-wise sense. The essential technique is to prove $(-\Delta)^s_p u(x)$ is uniformly bounded in the unit ball $B_1\subset\mathbb{R}^n$, where $u(x)=(1-|x|^2)^s_{+}$. Also we study the global H\"older…