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On Sobolev spaces of fractional order and ε-families of operators on spaces of homogeneous type

A. Gatto, Stephen Vági (1999)

Studia Mathematica

We introduce Sobolev spaces L α p for 1 < p < ∞ and small positive α on spaces of homogeneous type as the classes of functions f in L p with fractional derivative of order α, D α f , as introduced in [2], in L p . We show that for small α, L α p coincides with the continuous version of the Triebel-Lizorkin space F p α , 2 as defined by Y. S. Han and E. T. Sawyer in [4]. To prove this result we give a more general definition of ε-families of operators on spaces of homogeneous type, in which the identity operator is...

On some iterated means arising in homogenization theory

Dag Lukkassen, Jaak Peetre, Lars-Erik Persson (2004)

Applications of Mathematics

We consider iteration of arithmetic and power means and discuss methods for determining their limit. These means appear naturally in connection with some problems in homogenization theory.

On some iteration semigroups

Janusz Brzdęk (1995)

Archivum Mathematicum

Let F be a disjoint iteration semigroup of C n diffeomorphisms mapping a real open interval I ≠ ⌀ onto I . It is proved that if F has a dense orbit possesing a subset of the second category with the Baire property, then F = { f t f t ( x ) = f - 1 ( f ( x ) + t ) for every x ∈ I , t ∈ R } for some C n diffeomorphism f of I onto the set of all reals R . The paper generalizes some results of J.A.Baker and G.Blanton [3].

On some properties of Hamel bases and their applications to Marczewski measurable functions

François Dorais, Rafał Filipów, Tomasz Natkaniec (2013)

Open Mathematics

We introduce new properties of Hamel bases. We show that it is consistent with ZFC that such Hamel bases exist. Under the assumption that there exists a Hamel basis with one of these properties we construct a discontinuous and additive function that is Marczewski measurable. Moreover, we show that such a function can additionally have the intermediate value property (and even be an extendable function). Finally, we examine sums and limits of such functions.

Currently displaying 241 – 260 of 434