We prove that a $C^2$ diffeomorphism $f$ of a compact manifold $M$ satisfies Axiom A and the strong transversality condition if and only if it is H\"{o}lder stable, that is, any $C^1$ diffeomorphism $g$ of $M$ sufficiently $C^1$ close to $f$ is conjugate to $f$ by a homeomorphism which is H\"{o}lder on the whole manifold.

Jinpeng An

We study ordinary differential equations of the type $u^{(n)}(t)=f(u(t))$ with initial conditions $u(0) = u'(0) =... = u^{(m-1)}(0) = 0 $ and $u^{(m)}(0) \neq 0$ where $m \geq n$, no additional assumption is made on $f$. We establish some uniqueness results and show that $f$ is always H\"older continuous.

Yifei Pan Mei Wang Yu Yan

We use the H\"{o}lder inequality for mixed exponents to prove some optimal variants of the generalized Hardy--Littlewood inequality for $m$-linear forms on $\ell _{p}$ spaces with mixed exponents. Our results extend recent results of Araujo et al.

Nacib Albuquerque Tony Nogueira Daniel Nunez-Alarcon Daniel Pellegrino Pilar Rueda

We use sup-convolution to find upper approximations of a bounded $m$-subharmonic function on a compact K\"ahler manifold with nonnegative holomorphic bisectional curvature. As an application, we show the H\"older continuity of solutions to $\sigma_m$ equation when the right hand side is in $L^p$, $p>\frac{n}{m}$. All these results generalize to more general complex Hessian equations.

Jingrui Cheng Yulun Xu

Strong flares of TeV gamma-ray emission up to a level of ~5 Crab were detected by the Whipple 10 m atmospheric Cerenkov telescope from the BL Lacertae object 1ES1959+650 during May - July 2002. We report here the results of follow up observations during 2002 - 2003.

J. Holder

It is shown that an arbitrary function from $D\subset \R^n$ to $\R^m$ will become $C^{0,\alpha}$-continuous in almost every $x\in D$ after restriction to a certain subset with limit point $x$. For $n\geq m$ differentiability can be obtained. Examples show the H\"older exponent $\alpha=\min\{1,\frac{n}{m}\}$ is optimal.

Volker Elling

We present some identities related to the Cauchy-Schwarz inequality in complex inner product spaces. A new proof of the basic result on the subject of Strengthened Cauchy-Schwarz inequalities is derived using these identities. Also, an analogous version of this result is given for Strengthened H\"older inequalities.

J. M. Aldaz

We strengthen H\"older's inequality. The new family of sharp inequalities we obtain might be thought of as an analog of Pythagorean theorem for the $L^p$ spaces. Our reasonings rely upon Bellman functions of four variables.

Haakan Hedenmalm Dmitriy M. Stolyarov Vasily I. Vasyunin Pavel B. Zatitskiy

In this work, we consider a specific space of foliations with $C^1$ leaves and H\"older holonomies of the square $M=[0,1]^2$, with some topology and we show that a generic such foliation is non-absolutely continuous, furthermore, the conditional measures defined by Rokhlin disintegration are Dirac measures on the leaves. This space of foliations is motivated by the foliations that appear in hyperbolic systems and partially hyperbolic systems.

Enzo Fuentes

We study the regularity properties for solutions of a class of Schr\"odinger equations $(\Delta + V) u = 0$ on a stratified space $M$ endowed with an iterated edge metric. The focus is on obtaining optimal H\"older regularity of these solutions assuming fairly minimal conditions on the underlying metric and potential.

Kazuo Akutagawa Gilles Carron Rafe Mazzeo