Measure theoretic zero sets in infinite dimensional spaces and differentiability of Lipschitz mappings
Measuring asymptotic convexity
Meda inequality for rearrangements of the convolution on the Heisenberg group and some applications.
Mémoire sur les fonctions discontinues
Mémoire sur les intégrales définies, prises entre des limites imaginaires
Mémoire sur l'intégration d'une classe de fonctions transcendantes.
Meromorphic functions whose Julia sets contain a free Jordan arc.
Metric diophantine approximation in Julia sets of expanding rational maps
Metrically convex functions in normed spaces
Properties of metrically convex functions in normed spaces (of any dimension) are considered. The main result, Theorem 4.2, gives necessary and sufficient conditions for a function to be metrically convex, expressed in terms of the classical convexity theory.
Micro tangent sets of continuous functions
Motivated by the concept of tangent measures and by H. Fürstenberg’s definition of microsets of a compact set we introduce micro tangent sets and central micro tangent sets of continuous functions. It turns out that the typical continuous function has a rich (universal) micro tangent set structure at many points. The Brownian motion, on the other hand, with probability one does not have graph like, or central graph like micro tangent sets at all. Finally we show that at almost all points Takagi’s...
Midpoint convex functions majorized by midpoint concave functions.
Midpoint convex functions majorized by midpoint concave functions. (Short Communication).
Mild solutions for semilinear fractional differential equations.
Minimal pairs of bounded closed convex sets
The existence of a minimal element in every equivalence class of pairs of bounded closed convex sets in a reflexive locally convex topological vector space is proved. An example of a non-reflexive Banach space with an equivalence class containing no minimal element is presented.
Mittag-Leffler stability theorem for fractional nonlinear systems with delay.
Mixed Fractional Integration Operators in Mixed Weighted Hölder Spaces
MSC 2010: 26A33We study mixed Riemann-Liouville integrals of functions of two variables in Hölder spaces of different orders in each variables. We consider Hölder spaces defined both by first order differences in each variable and also by the mixed second order difference, the main interest being in the evaluation of the latter for the mixed fractional integral in both the cases where the density of the integral belongs to the Hölder class defined by usual or mixed differences. The obtained results...
Modified dyadic derivatives and integrals of fractional order on .
Modified log-Sobolev inequalities for convex functions on the real line. Sufficient conditions
We provide a mild sufficient condition for a probability measure on the real line to satisfy a modified log-Sobolev inequality for convex functions, interpolating between the classical log-Sobolev inequality and a Bobkov-Ledoux type inequality. As a consequence we obtain dimension-free two-level concentration results for convex functions of independent random variables with sufficiently regular tail decay. We also provide a link between modified log-Sobolev inequalities...
Modular inequalities for the Hardy averaging operator
If is the Hardy averaging operator - or some of its generalizations, then weighted modular inequalities of the form u (Pf) Cv (f) are established for a general class of functions . Modular inequalities for the two- and higher dimensional Hardy averaging operator are also given.
Moment measures of heavy-tailed renewal point processes: asymptotics and applications
We study higher-order moment measures of heavy-tailed renewal models, including a renewal point process with heavy-tailed inter-renewal distribution and its continuous analog, the occupation measure of a heavy-tailed Lévy subordinator. Our results reveal that the asymptotic structure of such moment measures are given by explicit power-law density functions. The same power-law densities appear naturally as cumulant measures of certain Poisson and Gaussian stochastic integrals. This correspondence...