Generalisations of -density
Generalization of a Theorem of Kusmin.
Generalization Of An Inequality Of G. Pólya Concerning The Eigenfrequences Of Vibrating Bodies
Generalizations of analytic and standard measurable spaces.
Generalizations of Castaing's theorem on selectors
Generalizations of Ostrowski inequality via biparametric Euler harmonic identities for measures.
Generalized Calderón conditions and regular orbit spaces
The construction of generalized continuous wavelet transforms on locally compact abelian groups A from quasi-regular representations of a semidirect product group G = A ⋊ H acting on L²(A) requires the existence of a square-integrable function whose Plancherel transform satisfies a Calderón-type resolution of the identity. The question then arises under what conditions such square-integrable functions exist. The existing literature on this subject leaves a gap between sufficient and necessary criteria....
Generalized convolutions II
Generalized dimension compression under mappings of exponentially integrable distortion
We prove a dimension compression estimate for homeomorphic mappings of exponentially integrable distortion via a modulus of continuity result by D. Herron and P. Koskela [Mappings of finite distortion: gauge dimension of generalized quasicircles, Illinois J. Math., 2003, 47(4), 1243–1259]. The essential sharpness of our estimate is demonstrated by an example.
Generalized fractional integral operators on weak Choquet spaces over quasi-metric measure spaces
We prove the boundedness of the generalized fractional maximal operator and the generalized fractional integral operator on weak Choquet spaces with respect to Hausdorff content over quasi-metric measure spaces.
Generalized Herglotz theorem in vector lattices
Generalized IFSs on noncompact spaces.
Generalized interval exchanges and the 2–3 conjecture
We introduce the notion of a generalized interval exchange induced by a measurable k-partition of [0,1). can be viewed as the corresponding restriction of a nondecreasing function on ℝ with . A is called λ-dense if λ(A i∩(a, b))>0 for each i and any 0≤ a< b≤1. We show that the 2–3 Furstenberg conjecture is invalid if and only if there are 2 and 3 λ-dense partitions A and B of [0,1), such that . We give necessary and sufficient conditions for this equality to hold. We show that...
Generalized iterated function systems, multifunctions and Cantor sets
Using a construction similar to an iterated function system, but with functions changing at each step of iteration, we provide a natural example of a continuous one-parameter family of holomorphic functions of infinitely many variables. This family is parametrized by the compact space of positive integer sequences of prescribed growth and hence it can also be viewed as a parametric description of a trivial analytic multifunction.
Generalized Lebesgue points for Sobolev functions
In many recent articles, medians have been used as a replacement of integral averages when the function fails to be locally integrable. A point in a metric measure space is called a generalized Lebesgue point of a measurable function if the medians of over the balls converge to when converges to . We know that almost every point of a measurable, almost everywhere finite function is a generalized Lebesgue point and the same is true for every point of a continuous function. We show...
Generalized Lusin sets with the Blackwell property
Generalized mean porosity and dimension.
Generalized Radon spaces which are not Radon.
Generalized transforms and convolutions.
Generalized Vitali systems of uniform type