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On Sharp Olsen’s and Trace Inequalities for Multilinear Fractional Integrals
Springer Science and Business Media LLC - Tập 59 - Trang 1039-1050 - 2022
We establish a sharp Olsen type inequality
$ \big \| g {\mathcal {I}}_{\alpha }(f_{1}, {\dots } , f_{m}) \big \|_{{L^{q}_{r}} } \leq C \big \| g \big \|_{L^{q}_{\ell } } \prod\limits_{j=1}^{m} \big \| f_{j}\big \|_{L^{p_{j}}_{s_{j}}} $
for multilinear fractional integrals
...... hiện toàn bộ
Well-posedness and Large Deviations of the Stochastic Modified Camassa-Holm Equation
Springer Science and Business Media LLC - Tập 45 - Trang 331-354 - 2016
In this paper, the stochastic modified Camassa-Holm (MCH) equation is concerned. Firstly, the local well-posedness for this equation is established by the trilinear estimates to the approximate solutions. Then the large deviation principle (LDP) for the regularized stochastic MCH is obtained by the weak convergence approach. To get the LDP for stochastic MCH, some exponentially equivalents of the ...... hiện toàn bộ
Recurrent Dirichlet Forms and Markov Property of Associated Gaussian Fields
Springer Science and Business Media LLC - Tập 49 - Trang 609-633 - 2017
For the extended Dirichlet space
$\mathcal {F}_{e}$
of a general irreducible recurrent regular Dirichlet form
...... hiện toàn bộ
Exponential Contraction in Wasserstein Distances for Diffusion Semigroups with Negative Curvature
Springer Science and Business Media LLC - Tập 53 - Trang 1123-1144 - 2020
Let Pt be the (Neumann) diffusion semigroup Pt generated by a weighted Laplacian on a complete connected Riemannian manifold M without boundary or with a convex boundary. It is well known that the Bakry-Emery curvature is bounded below by a positive constant ≪> 0 if and only if
$$W_{p}(\mu_{1}P_{t}, \mu_{2}P_{t})\leq e^{-\ll t} W_{p} (\mu_{1},\mu_{2}),\ \ t\geq 0, p\geq 1 $$
holds for all proba...... hiện toàn bộ
The Berezin Transform of Toeplitz Operators on the Weighted Bergman Space
Springer Science and Business Media LLC - Tập 57 - Trang 263-281 - 2021
In this paper, we obtain some interesting reproducing kernel estimates and some Carleson properties that play an important role. We characterize the bounded and compact Toeplitz operators on the weighted Bergman spaces with Békollé-Bonami weights in terms of Berezin transforms. Moreover, we estimate the essential norm of them assuming that they are bounded.
Harnack Inequalities and Applications for Ornstein–Uhlenbeck Semigroups with Jump
Springer Science and Business Media LLC - - 2011
The Harnack inequality established in Röckner and Wang (J Funct Anal 203:237–261, 2003) for generalized Mehler semigroup is improved and generalized. As applications, the log-Harnack inequality, the strong Feller property, the hyper-bounded property, and some heat kernel inequalities are presented for a class of O-U type semigroups with jump. These inequalities and semigroup properties are indeed ...... hiện toàn bộ
Dual Spaces for Weak Martingale Hardy Spaces Associated with Rearrangement-Invariant Spaces
Springer Science and Business Media LLC -
Problèmes elliptiques à frontière libre axi-symétriques: Estimation du diamètre de la section au moyen de la capacité
Springer Science and Business Media LLC - Tập 5 - Trang 61-72 - 1996
Le but de cet article est d'estimer la capacité d'un pétit segment [a(1−ε), a(1+ε)]×{z=0} du démi-plan П := {x = (r, z)|r > 0, z ∈ ℝ} de ℝ2 par rapport à la capacité définie par la norme
$$\left\| u \right\|_{H_L }^2 = \int_\prod u Lu r dr dz: = \int_\prod \{ u_r^2 + u_z^2 \} r^{ - k} dr dz$$
...... hiện toàn bộ
Radially Symmetric Functions as Fixed Points of some Logarithmic Operators
Springer Science and Business Media LLC - Tập 9 - Trang 83-89 - 1998
In this note we show that for f ∈ C((0,∞); R+) ∩ C1 ((0,∞)) with support in [0,∞), if a function u ∈ C1(R2) is such that support (u+) is compact and u(x) = ∫R2 f(u(y)) log 1/(|x-y|)dy ∀ x, then u is radial. This result is important for some free boundary problems in R2 or some axisymmetric ones in Rn.
Théorie du potentiel pour des opérateurs elliptiques non linéaires du second ordre à coefficients discontinus
Springer Science and Business Media LLC - Tập 15 - Trang 255-271 - 2001
Let Ω a open subset of ℝ
n
, n⩾3, and Ω⊂
$$\overline \omega$$
⊂Ω an open. Existence and unicity are proved for the Dirichlet problem
$$\left\{ \begin{gathered} \mathcal{L}u: = - \sum\nolimits...... hiện toàn bộ
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