Related papers: Sharp L^p estimates on BMO

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…

We consider $L^p$-$L^q$ estimates for the spherical harmonic projection operators and obtain sharp bounds on a certain range of $p$, $q$. As an application, we provide a proof of off-diagonal Carleman estimates for the Laplacian, which…

We give characterizations of (quasi-)plurisubharmonic functions in terms of $L^p$-estimates of $\bar\partial$ and $L^p$-extensions of holomorphic functions.

In 2003, Del Pino and Dolbeault [14] and Gentil [19] investigated, independently, best constants and extremals associated to Euclidean Lp-entropy inequalities for p > 1. In this work, we present some contributions in the Riemannian context.…

We introduce the mixed-norm amalgam spaces $(L^{\vec{p}},L^{\vec{s}})(\mathbb{R}^n)$ and $(L^{\vec{p}},L^{\vec{s}})^{\alpha}(\mathbb{R}^n)$, and show their some basic properties. In addition, we find the predual…

We prove a duality theorem the computation of certain Bellman functions is usually based on. As a byproduct, we obtain sharp results about the norms of monotonic rearrangements. The main novelty of our approach is a special class of…

For the homogeneous Boltzmann equation with (cutoff or non cutoff) hard potentials, we prove estimates of propagation of Lp norms with a weight $(1+ |x|^2)^q/2$ ($1 < p < +\infty$, $q \in \R\_+$ large enough), as well as appearance of such…

In this paper, we obtain boundary Harnack estimates and comparison theorem for nonnegative solutions to the linearized Monge-Amp\`ere equations under natural assumptions on the domain, Monge-Amp\`ere measures and boundary data. Our results…

In this paper we investigate the regularity properties of weighted Bergman projections for smoothly bounded pseudo-convex domains of finite type in $\mathbb{C}^{n}$. The main result is obtained for weights equal to a non negative rational…

We give a general method to obtain from the integral restrictions of functions sharp pointwise and uniform estimates of these functions. This scheme is illustrated by the examples for Fock\,--\,Bargmann spaces of entire functions of several…

The relationship between the operator norms of fractional integral operators acting on weighted Lebesgue spaces and the constant of the weights is investigated. Sharp boundsare obtained for both the fractional integral operators and the…

We consider BMO spaces of operator-valued functions, among them the space of operator-valued functions $B$ which define a bounded paraproduct on $L^2(H)$. We obtain several equivalent formulations of $\|\pi_B\|$ in terms of the norm of the…

Existence and boundary regularity away from the corners are established for two-dimensional Monge-Amp\`{e}re equations on convex polytopes with Guillemin boundary conditions. An important step is to derive an expansion in terms of functions…

We investigate $L^p$ regularity of weighted Bergman projections on the unit disc and $L^p$ regularity of ordinary Bergman projections in higher dimensions.

We study the Lorentz spaces $L^{p,s}(R,\mu)$ in the range $1<p<s\le \infty$, for which the standard functional $$ ||f||_{p,s}=(\int_0^\infty (t^{1/p}f^*(t))^s\frac{dt}{t})^{1/s} $$ is only a quasi-norm. We find the optimal constant in the…

We discuss the L^p-boundedness of maximal singular integrals in the plane over a finite set V of N directions. Logarithmic bounds are established for a set V of arbitrary structure in the 2<=p<infinity range. Sharp bounds are proved for…

Modular equations occur in number theory, but it is less known that such equations also occur in the study of deformation properties of quasiconformal mappings. The authors study two important plane quasiconformal distortion functions,…

Ratios of integrals can be bounded in terms of ratios of integrands under certain monotonicity conditions. This result, related with L'H\^{o}pital's monotone rule, can be used to obtain sharp bounds for cumulative distribution functions. We…

Let $V\subset\R^m$ be a centrally symmetric convex body and let $V^*\subset\R^m$ be its polar. We prove limit relations between the sharp constants in the multivariate Markov-Bernstein-Nikolskii type inequalities for algebraic polynomials…

We obtain sharp ranges of $L^p$-boundedness for domains in a wide class of Reinhardt domains representable as sub-level sets of monomials, by expressing them as quotients of simpler domains. We prove a general transformation law relating…