Approximation Properties of Some Types of Linear Means in Space L p(x) 2π

Abstract

An inverse spectral problem is studied for variable orders differential operators on compact star-type graphs. A uniqueness theorem of recovering potentials from the Weyl matrices is provided. A constructive solution of the inverse problem is obtained.

Trigonometric Approximation of Functions from $$L_{2\pi }^{p(x)}$$

“…where α ∈ (0, 1] and p = p(x) ∈ Π 2π . From Theorem 4 the results of [1][2][3][4][5]7] and [11,Theorem 5 (v)], [6,Theorem 5 (vi)] follow at once in the more general and improved forms. More precisely, in the mentioned papers [2][3][4] there is considered the following modulus of continuity…”

“…greater than Ωf (δ) p and therefore the class Lip p (ω, M ) constructed by modulus Ωf (δ) p is wider then such one constructed by Ω p f (δ). Moreover, in these papers and also in [7] there is the assumption p (x) ≥ p − > 1, since for p − = 1 the quantity Ω p f (δ) may not tend to 0 when δ → 0 for some f ∈ L p 2π . In the papers [1,5], [11,Theorem 5 (…”

On Uniform Boundedness of Some Families of Integral Convolution Operators in Weighted Variable Exponent Lebesgue Spaces

“…, где были получены достаточные условия на ядра, при которых обеспечивалась равномерная ограниченность. Вышеупомянутый результат был перенесен на многомерный случай в [7]. Схожая задача рассматривалась еще и в работе [8].…”