Related papers: Best constants in reverse Riesz-type inequalities …

We consider Schroedinger operators on metric cones whose cross section is a closed Riemannian manifold $(Y, h)$ of dimension $d-1 \geq 2$. Thus the metric on the cone $M = (0, \infty)_r \times Y$ is $dr^2 + r^2 h$. Let $\Delta$ be the…

The paper concerns the magnetic Schr\"odinger operator on $R^n$. We prove some $L^p$ estimates on the Riesz transforms and we establish some related maximal inequalities. The conditions that we arrive at, are essentially based on the…

Let $L=-\sum_{i,j=1}^n a_{ij}D_iD_j$ be the elliptic operator in non-divergence form with smooth real coefficients satisfying uniformly elliptic condition. Let $W$ be the global nonnegative adjoint solution. If $W\in A_2$, we prove that the…

Recently, Nagy-To\'okos and Totik-Varga proved an asymptotically sharp $L^{p}$ Bernstein type inequality on union of finitely many intervals. We extend this inequality to the case when the power $p$ is between $0$ and $1$; such sharp…

Let $X$ be a non-compact symmetric space of dimension $n$. We prove that if $f\in L^{p}(X)$, $1\leq p\leq 2$, then the Riesz means $S_{R}^{z}\left( f\right)$ converge to $f$ almost everywhere as $R\rightarrow \infty $, whenever…

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…

In this paper, we obtained the Dunkl analogy of classical Lp Hardy inequality for $p > N + 2\gamma$ with sharp constant $\left(\frac{p-N-2\gamma}{p}\right)^{p}$, where $2\gamma$ is the degree of weight function associated with Dunkl…

We prove sharp power-weighted strong type, weak type and restricted weak type inequalities for the heat and Poisson integral maximal operators, Riesz transform and a Littlewood-Paley type square function, emerging naturally in the harmonic…

We obtain Lipschitz estimates for bounded minimizers of functionals with nonstandard $(p,q)$-growth satisfying the dimension-independent restriction $q<p+2$ with $p \geq 2$. This relation improves existing restrictions when $p \leq N-1$,…

Let $X$ be a supermartingale starting from $0$ which has only nonnegative jumps. For each $0<p<1$ we determine the best constants $c_p$, $C_p$ and $\mathfrak{c}_p$ such that $$ \,\,\,\,\sup_{t\geq 0}\left|\left|X_t\right|\right|_p\leq…

The Blaschke Santal\'o inequality and the $L_p$ affine isoperimetric inequalities are major inequalities in convex geometry and they have a wide range of applications. Functional versions of the Blaschke Santal\'o inequality have been…

We recall that $w\in C_{p}^{+}$ if there exist $\varepsilon>0$ and $C>0$ such that for any $a<b<c$ with $c-b<b-a$ and any measurable set $E\subset(a,b)$, the following holds \[ \int_{E}w\leq…

We derive sharp Adams inequalities with exact growth condition for the Riesz potential as well as more general Riesz-like potentials on R^n. We also obtain Moser-Trudinger inequalities with exact growth condition for the fractional…

In this paper, we obtain the desired noncommutative maximal inequalities of the truncated Calder\'on-Zygmund operators of non-convolution type acting on operator-valued $L_p$-functions for all $1<p<\infty$, answering a question left open in…

We present a unified approach to improved $L^p$ Hardy inequalities in $\R^N$. We consider Hardy potentials that involve either the distance from a point, or the distance from the boundary, or even the intermediate case where distance is…

We study the norm of point evaluation at the origin in the Paley--Wiener space $PW^p$ for $0 < p < \infty$, i. e., we search for the smallest positive constant $C$, called $\mathscr{C}_p$, such that the inequality $|f(0)|^p \leq C…

For $-1\le B<A\le 1$, let $\mathcal{S}^*(A,B)$ denote the class of normalized analytic functions $f(z)= z+\sum_{n=2}^{\infty}a_n z^n$ in $|z|<1$ which satisfy the subordination relation $zf'(z)/f(z)\prec (1+Az)/(1+Bz)$ and $\Sigma^*(A,B)$…

We study the boundedness problem for maximal operators $\mathbb{M}$ associated to averages along families of finite type curves in the plane, defined by $$\mathbb{M}f(x) \, := \, \sup_{1 \leq t \leq 2} \left|\int_{\mathbb{C}} f(x-ty) \,…

We derive optimal dimension independent constants in the classical Khintchine inequality between the $p$th and fourth moment for $p\ge 4$. As an application we deduce stability estimates for the Khintchine inequality between the $p$th and…

Strong convergence and convergence in probability were generalized to the setting of a Riesz space with conditional expectation operator, $T$, in [{{\sc Y. Azouzi, W.-C. Kuo, K. Ramdane, B. A. Watson}, {Convergence in Riesz spaces with…