On the Factor Opposing the Lebesgue Norm in Generalized Grand Lebesgue Spaces

Generalized Lebesgue Spaces and Application to Statistics

Statistics requires consideration of the “ideal estimates” defined through the posterior mean of fractional powers of finite measures. In this paper we study L1= , the linear space spanned by th power of finite measures, 2 (0; 1). It is shown that L1= generalizes the Lebesgue function space L1= ( ), and shares most of its important properties: It is a uniformly convex (hence reflexive) Banach s...

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...

Decomposition of Lebesgue Spaces

Interpolation orbits in the Lebesgue spaces

This paper is devoted to description of interpolation orbits with respect to linear operators mapping an arbitrary couple of L p spaces with weights {L p 0 (U 0), L p 1 (U 1)} into an arbitrary couple {L q 0 (V 0), L q 1 (V 1)}, where 1 ≤ p 0 , p 1 , q 0 , q 1 ≤ ∞. By L p (U) we denote the space of measurable functions f on a measure space M such that f U ∈ L p with the norm f Lp(U) = f U Lp. }...

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.