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Modified log-Sobolev inequalities for convex functions on the real line. Sufficient conditions

Radosław Adamczak, Michał Strzelecki (2015)

Studia Mathematica

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

Hans P. Heinig (1999)

Mathematica Bohemica

If P 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 φ . Modular inequalities for the two- and higher dimensional Hardy averaging operator are also given.

Moduli of smoothness of functions and their derivatives

Z. Ditzian, S. Tikhonov (2007)

Studia Mathematica

Relations between moduli of smoothness of the derivatives of a function and those of the function itself are investigated. The results are for L p ( T ) and L p [ - 1 , 1 ] for 0 < p < ∞ using the moduli of smoothness ω r ( f , t ) p and ω φ r ( f , t ) p respectively.

Monotonicity in Banach function spaces

Sinnamon, Gord (2007)

Nonlinear Analysis, Function Spaces and Applications

This paper is an informal presentation of material from [28]–[34]. The monotone envelopes of a function, including the level function, are introduced and their properties are studied. Applications to norm inequalities are given. The down space of a Banach function space is defined and connections are made between monotone envelopes and the norms of the down space and its dual. The connection is shown to be particularly close in the case of universally rearrangement invariant spaces. Next, two equivalent...

Monotonicity of certain functionals under rearrangement

Adriano Garsia, Eugène Rodemich (1974)

Annales de l'institut Fourier

We show here that a wide class of integral inequalities concerning functions on [ 0 , 1 ] can be obtained by purely combinatorial methods. More precisely, we obtain modulus of continuity or other high order norm estimates for functions satisfying conditions of the type ∫ 0 1 ∫ 0 1 Ψ f ( x ) - f ( y ) p ( x - y ) d x d y &lt; ∞ where Ψ ( u ) and p ( u ) are monotone increasing functions of | u | .Several applications are also derived. In particular these methods are shown to yield a new condition for path continuity of general stochastic processes

Monotonicity of generalized weighted mean values

Alfred Witkowski (2004)

Colloquium Mathematicae

The author gives a new simple proof of monotonicity of the generalized extended mean values M ( r , s ) = ≤ ( ( ∫ f s d μ ) / ( ∫ f r d μ ) ) 1 / ( s - r ) introduced by F. Qi.

Currently displaying 681 – 700 of 1525