Sobolev spaces, Lebesgue points and maximal functions

Spanning and Sampling in Lebesgue and Sobolev Spaces

We establish conditions on ψ under which the small-scale affine system {ψ(ajx− k) : j ≥ J, k ∈ Zd} spans the Lebesgue space L(R) and the Sobolev space W(R), for 1 ≤ p < ∞ and J ∈ Z. The dilation matrices aj are expanding (meaning limj→∞ ‖a−1 j ‖ = 0) but they need not be diagonal. For spanning L our result assumes ∫ Rd ψ dx 6= 0 and, when p > 1, that the periodization of |ψ| or of 1{ψ 6=0} is b...

Maximal and partial points in formal spaces

The class of points in a set-presented formal topology is a set, if all points are maximal. To prove this constructively a strengtening of the dependent choice principle to in nite wellfounded trees is used. MSC: 03F65, 54A05.

Maximal Regularity for Flexible Structural Systems in Lebesgue Spaces

We study abstract equations of the form λu′′′ t u′′ t c2Au t c2μAu′ t f t , 0 < λ < μ which is motivated by the study of vibrations of flexible structures possessing internal material damping. We introduce the notion of α; β; γ -regularized families, which is a particular case of a; k regularized families, and characterize maximal regularity in L-spaces based on the technique of Fourier multipl...

Extreme points of the unit cell in Lebesgue-Bochner functions spaces

Extreme points of the unit cell Lebesgue-Bochner function spaces