Nous précisons la classe de différentiabilité de où désigne une fonction positive de classe , -plate sur l’ensemble de ses zéros, et un réel, ; de plus, nous étudions l’existence locale d’une racine -ième de classe , pour une fonction de classe admettant une racine -ième formelle en chaque point.
For a function the notion of p-mean variation of order 1, is defined. It generalizes the concept of F. Riesz variation of functions on the real line ℝ¹ to ℝⁿ, n > 1. The characterisation of the Sobolev space in terms of is directly related to the characterisation of by Lipschitz type pointwise inequalities of Bojarski, Hajłasz and Strzelecki and to the Bourgain-Brezis-Mironescu approach.
We present comparison theorems for the weighted quasi-arithmetic means and for weighted Bajraktarević means without supposing in advance that the weights are the same.
In this paper we consider some spaces of differentiable multifunctions, in particular the generalized Orlicz-Sobolev spaces of multifunctions, we study completeness of them, and give some theorems.
Let 𝓐(ℝ) and 𝓔(ℝ) denote respectively the ring of analytic and real entire functions in one variable. It is shown that if 𝔪 is a maximal ideal of 𝓐(ℝ), then 𝓐(ℝ)/𝔪 is isomorphic either to the reals or a real closed field that is an η₁-set, while if 𝔪 is a maximal ideal of 𝓔(ℝ), then 𝓔(ℝ)/𝔪 is isomorphic to one of the latter two fields or to the field of complex numbers. Moreover, we study the residue class rings of prime ideals of these rings and their Krull dimensions. Use is made of...
The McShane and Kurzweil-Henstock integrals for functions taking values in a locally convex space are defined and the relations with other integrals are studied. A characterization of locally convex spaces in which Henstock Lemma holds is given.