On small Lebesgue spaces

Decomposition of Lebesgue Spaces

On isomorphism of two bases in Morrey-Lebesgue type spaces

Double system of exponents with complex-valued coefficients is considered. Under some conditions on the coefficients, we prove that if this system forms a basis for the Morrey-Lebesgue type space on $left[-pi , pi right]$, then it is isomorphic to the classical system of exponents in this space.

Affine Synthesis onto Lebesgue and Hardy Spaces

The affine synthesis operator Sc = P j>0 P k∈Zd cj,kψj,k is shown to map the mixed-norm sequence space `(`) surjectively onto L(R) under mild conditions on the synthesizer ψ ∈ L(R), 1 ≤ p < ∞, with R Rd ψ dx = 1. Here ψj,k(x) = |det aj |ψ(ajx−k), and the dilation matrices aj expand, for example aj = 2I . Affine synthesis further maps a discrete mixed Hardy space `(h) onto H(R). Therefore the H-...

The Sampling Theorem in Variable Lebesgue Spaces

hold. The facts above are well-known as the classical Shannon sampling theorem initially proved by Ogura [10]. Ashino and Mandai [1] generalized the sampling theorem in Lebesgue spaces L0(R) for 1 < p0 < ∞. Their generalized sampling theorem is the following. Theorem 1.1 ([1]). Let r > 0 and 1 < p0 < ∞. Then for all f ∈ L 0(R) with supp f̂ ⊂ [−rπ, rπ], we have the norm inequality C p r ‖f‖Lp0(Rn...

Lipschitzian Properties of Integral Functionals on Lebesgue Spaces

We give a complete characterization of integral functionals which are Lipschitzian on a Lebesgue space Lp with p finite. When the measure is atomless, we characterize the integral functionals which are locally Lipschitzian on such Lebesgue spaces Lp. In every cases, the Lipchitzian properties of the integral functional are described by Lipschitzian properties of the integrand. Mathematics Subje...