Related papers: $L^p$ estimates for a singular entangled quadrilin…

The paper is a comprehensive study of the $L_p$ and the Schauder estimates for higher-order divergence type parabolic systems with discontinuous coefficients in the half space and cylindrical domains with conormal derivative boundary…

By using some recent results for divergence form equations, we study the $L_p$-solvability of second-order elliptic and parabolic equations in nondivergence form for any $p\in (1,\infty)$. The leading coefficients are assumed to be in…

In this paper, we study both elliptic and parabolic equations in non-divergence form with singular degenerate coefficients. Weighted and mixed-norm $L_p$-estimates and solvability are established under some suitable partially weighted BMO…

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 introduce a notion of geometric tempering using exponentially-dampened Mittag-Leffler tempering functions and closely investigate the univariate case. Characteristic exponents and cumulants are calculated, as well as spectral densities.…

We prove several off-diagonal and pointwise estimates for singular integral operators that extend compactly on $L^{p}(\mathbb R^{n})$.

This paper investigates $L^p$-estimates for solutions to the wave equation perturbed by a scaling-critical partial inverse-square potential. We study a model in which the singularity of the potential appears only in a subset of the…

We prove $L^p-L^q$ Carleman estimates with convex power weights $|x|^\beta$, extending previous work by J. O. Str\"omberg.

We establish boundary regularity estimates for elliptic systems in divergence form with VMO coefficients. Additionally, we obtain nondegeneracy estimates of the Hopf-Oleinik type lemma for elliptic equations. In both cases, the moduli of…

We establish new $p$-estimates for the norm of the generalized Beurling--Ahlfors transform $\mathcal{S}$ acting on form-valued functions. Namely, we prove that $\norm{\mathcal{S}}_{L^p(\R^n;\Lambda)\to L^p(\R^n;\Lambda)}\leq n(p^{*}-1)$…

This expository note, written for the proceedings of ICCM 2023, presents recent work [arXiv:2004.13894]. We particularly prove an Carleman estimate on conic manifolds, using a multiple-weight Carleman argument.

We improve the $L^{p}\rightarrow L^p$ restriction estimate in $\mathbb{R}^3$ to the range $p>3+3/14$, based on some Kakeya type incidence estimates and the refined decoupling theorem.

This paper develops an approach to the evaluation of quadratic Euler sums that involve harmonic numbers. The approach is based on simple integral computations of polyloga- rithms. By using the approach, we establish some relations between…

For the fourth Painlev\'e transcendents we derive elliptic asymptotic representations, which were announced by late Professor Kapaev without proofs. Then we newly obtain related results including the correction function.

This survey paper contains a detailed self-contained introduction to Korovkin-type theorems and to some of their applications concerning the approximation of continuous functions as well as of L^p-functions, by means of positive linear…

In this work, we obtain quantitative estimates of the continuity constant for the $L^p$ maximal regularity of relatively continuous nonautonomous operators $\mathbb{A} : I \longrightarrow \mathcal{L}(D,X)$, where $D \subset X$ densely and…

We prove old and new $L^p$ bounds for the quartile operator, a Walsh model of the bilinear Hilbert transform, uniformly in the parameter that models degeneration of the bilinear Hilbert transform. We obtain the full range of exponents that…

First-order methods are often analyzed via their continuous-time models, where their worst-case convergence properties are usually approached via Lyapunov functions. In this work, we provide a systematic and principled approach to find and…

A sharp quantitative version of the $L_p-$mixed volume inequality is established. This is achieved by exploiting an improved Jensen inequality. This inequality is a generalization of Pinsker-Csisz\'ar-Kullback inequality for the Tsallis…

We prove sharp smoothing properties of the averaging operator defined by convolution with a measure on a smooth nondegenerate curve $\gamma$ in $\mathbb R^d$, $d\ge 3$. Despite the simple geometric structure of such curves, the sharp…