Year: 2025
Type: article
Abstract: This paper introduces the concept of a t-basis generated by some bilinear mapping t(·;·). It is considered the vector-valued class Lp(X) := Lp(J; X), 1 ≤ p < +∞, where J = [−π, π] and X is a Banach space with the UMD property, and it is proven that the classical system of exponents {eint}n∈ℤ forms a t-basis for Lp(X), 1 < p < +∞. Using this fact, the Hardy vector classes nHp±(X), 1 < p < +∞, different from the classical ones, are defined, and an equivalent definition of these classes is given and some of their properties are studied. In addition, the concept of t-Riesz property of a system of exponentials is introduced in Lp(X), 1 < p < +∞, and it is proved that this system has the t-Riesz property. A new method is given for establishing the Plemelj–Sokhotski formulas for X-valued Cauchy type integrals when X has the UMD property. An abstract analogue of the “1/4-Kadets” theorem is obtained for L2(H), where H is a Hilbert space.
Source: TURKISH JOURNAL OF MATHEMATICS
Authors: BILAL BILALOV, SABINA RAHIB SADIGOVA
Language: English
Topic: Advanced Banach Space Theory
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4410430644