相关论文: Sharp inequalities for linear combinations of orth…

Sharp estimates of solutions of the classical heat equation are proved in $L^p$ norms on the real line.

We prove a sharp H\"older estimate for solutions of linear two-dimensional, divergence form elliptic equations with measurable coefficients, such that the matrix of the coefficients is symmetric and has {\em unit determinant}. Our result…

We give a partial negative answer to a question left open in a previous work by Brasco and the first and third-named authors concerning the sharp constant in the fractional Hardy inequality on convex sets. Our approach has a geometrical…

We give several sharp estimates for a class of combinations of second order Riesz transforms on Lie groups ${G}={G}_{x} \times {G}_{y}$ that are multiply connected, composed of a discrete abelian component ${G}_{x}$ and a connected…

The inverse tangent function can be bounded by different inequalities, for example by Shafer's inequality. In this publication, we propose a new sharp double inequality, consisting of a lower and an upper bound, for the inverse tangent…

In this paper we study sharp pointwise inequalities for maximal operators. In particular, we strengthen DeVore's inequality for the moduli of smoothness and a logarithmic variant of Bennett--DeVore--Sharpley's inequality for rearrangements.…

Sharp asymptotic for norms of Fourier projections on two-point homogeneous manifolds (the real sphere, the real, complex and quaternionic projective spaces and the Cayley elliptic plain) are established. These results extend sharp…

We establish sharp affine weighted $L^p$ Sobolev type inequalities by using the $L_p$ Busemann-Petty centroid inequality proved by Lutwak, Yang and Zhang. Our approach consists in combining in a convenient way the latter one with a suitable…

As a corollary to our main result we deduce sharp A_p$ inequalities for T being either the Hilbert transform in dimension d=1, the Beurling transform in dimension d=2, or a Riesz transform in any dimension d\ge 2. For T_{\ast} the maximal…

We study $L^p$-Sobolev regularity estimate for the restricted X-ray transforms generated by nondegenerate curves. Making use of the inductive strategy in the recent work by the authors, we establish the sharp $L^p$-regularity estimates for…

We establish optimal L^p bounds for the nontangential maximal function of the gradient of the solution to a second order elliptic operator in divergence form, possibly non-symmetric, with bounded measurable coefficients independent of the…

Let $V\subset\R^m$ be a convex body, symmetric about all coordinate hyperplanes, and let $\PP_{aV},\, a\ge 0$, be a set of all algebraic polynomials whose Newton polyhedra are subsets of $aV$. We prove a limit equality as $a\to \iy$ between…

We dominate non-integral singular operators by adapted sparse operators and derive optimal norm estimates in weighted spaces. Our assumptions on the operators are minimal and our result applies to an array of situations, whose prototype are…

For the fractional Laplacian we give Hardy inequality which is optimal in $L^p$ for $1<p<\infty$. As an application, we explicitly characterize the contractivity of the corresponding Feynman-Kac semigroups on $L^p$.

In this paper, we generalize Cristinel Mortici's results on Wilker-Cusa-Huygens inequalities using stratified families of functions and SimTheP - a system for automated proving of MTP inequalities.

We establish local $(L^p,L^q)$ mapping properties for averages on curves. The exponents are sharp except for endpoints.

We construct new optimal $L^p$ Hardy-type inequalities for elliptic Schr\"odinger-type operators

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…

In this article we study the Schr\"odinger equation associated with Harmonic oscillator in the form of Strichartz type inequality. We give simple proofs for Strichartz type inequalities using purely the $L^2 \to L^p$ operator norm estimates…

In this paper, we obtain sharp remainder terms for the Hardy-Poincar\'e inequalities with general non-radial weights in the setting of Baouendi-Grushin vector fields (see Theorem 2.5). It is worth emphasizing that all of our results are new…