scholarly journals Bernstein inequalities via the heat semigroup

2021 ◽  
Author(s):  
Rafik Imekraz ◽  
El Maati Ouhabaz
Keyword(s):  
Heat Semigroup ◽  
Bernstein Inequalities

scholarly journals Heat kernels of the discrete Laguerre operators

2021 ◽  
Vol 111 (2) ◽  
Author(s):  
Aleksey Kostenko
Keyword(s):  
Hardy Inequality ◽  
Jacobi Polynomials ◽  
Heat Kernels ◽  
The Other ◽  
Heat Semigroup ◽  
Stochastic Completeness ◽  
Markovian Semigroup ◽  
Other Hand ◽  
The One

AbstractFor the discrete Laguerre operators we compute explicitly the corresponding heat kernels by expressing them with the help of Jacobi polynomials. This enables us to show that the heat semigroup is ultracontractive and to compute the corresponding norms. On the one hand, this helps us to answer basic questions (recurrence, stochastic completeness) regarding the associated Markovian semigroup. On the other hand, we prove the analogs of the Cwiekel–Lieb–Rosenblum and the Bargmann estimates for perturbations of the Laguerre operators, as well as the optimal Hardy inequality.

SOME ESTIMATES FOR POLYNOMIALS

2009 ◽  
Vol 02 (03) ◽  
pp. 425-434
Author(s):  
Tatsuhiro Honda ◽  
Mitsuhiro Miyagi ◽  
Masaru Nishihara ◽  
Seiko Ohgai ◽  
Mamoru Yoshida
Keyword(s):  
Trigonometric Polynomials ◽  
Alternative Proof ◽  
Bernstein Inequalities

We give an elementary alternative proof of the Bernstein inequalities and the Szegö inequalities for trigonometric polynomials or polynomials.

scholarly journals A generalized conservation property for the heat semigroup on weighted manifolds

2019 ◽  
Vol 377 (3-4) ◽  
pp. 1673-1710
Author(s):  
Jun Masamune ◽  
Marcel Schmidt
Keyword(s):  
Heat Semigroup ◽  
Conservation Property ◽  
Weighted Manifolds

Boundedness of Differential Transforms for Heat Semigroups Generated by Schrödinger Operators

2020 ◽  
pp. 1-34
Author(s):  
Zhang Chao ◽  
José L. Torrea
Keyword(s):  
Maximal Operator ◽  
Singular Integrals ◽  
Heat Semigroup ◽  
Real Sequence ◽  
Differential Transform ◽  
Intermediate Size ◽  
Heat Semigroups ◽  
Image Position ◽  
Reverse Hölder ◽  
Littlewood Maximal Operator

Abstract In this paper we analyze the convergence of the following type of series $$\begin{eqnarray}T_{N}^{{\mathcal{L}}}f(x)=\mathop{\sum }_{j=N_{1}}^{N_{2}}v_{j}\big(e^{-a_{j+1}{\mathcal{L}}}f(x)-e^{-a_{j}{\mathcal{L}}}f(x)\big),\quad x\in \mathbb{R}^{n},\end{eqnarray}$$ where ${\{e^{-t{\mathcal{L}}}\}}_{t>0}$ is the heat semigroup of the operator ${\mathcal{L}}=-\unicode[STIX]{x1D6E5}+V$ with $\unicode[STIX]{x1D6E5}$ being the classical laplacian, the nonnegative potential $V$ belonging to the reverse Hölder class $RH_{q}$ with $q>n/2$ and $n\geqslant 3$ , $N=(N_{1},N_{2})\in \mathbb{Z}^{2}$ with $N_{1}<N_{2}$ , ${\{v_{j}\}}_{j\in \mathbb{Z}}$ is a bounded real sequences, and ${\{a_{j}\}}_{j\in \mathbb{Z}}$ is an increasing real sequence. Our analysis will consist in the boundedness, in $L^{p}(\mathbb{R}^{n})$ and in $BMO(\mathbb{R}^{n})$ , of the operators $T_{N}^{{\mathcal{L}}}$ and its maximal operator $T^{\ast }f(x)=\sup _{N}T_{N}^{{\mathcal{L}}}f(x)$ . It is also shown that the local size of the maximal differential transform operators (with $V=0$ ) is the same with the order of a singular integral for functions $f$ having local support. Moreover, if ${\{v_{j}\}}_{j\in \mathbb{Z}}\in \ell ^{p}(\mathbb{Z})$ , we get an intermediate size between the local size of singular integrals and Hardy–Littlewood maximal operator.

scholarly journals Besov class via heat semigroup on Dirichlet spaces II: BV functions and Gaussian heat kernel estimates

2020 ◽  
Vol 59 (3) ◽  
Author(s):  
Patricia Alonso-Ruiz ◽  
Fabrice Baudoin ◽  
Li Chen ◽  
Luke Rogers ◽  
Nageswari Shanmugalingam ◽  
...  
Keyword(s):  
Heat Kernel ◽  
Heat Semigroup ◽  
Dirichlet Spaces ◽  
Kernel Estimates ◽  
Besov Class ◽  
Heat Kernel Estimates ◽  
Bv Functions
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