Research Information System
Turkish Journal of Mathematics, vol.49, no.3, pp.261-286, 2025 (SCI-Expanded, Scopus)
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 (Formula presented) forms a t-basis for Lp (X), 1 < p < +∞. Using this fact, the Hardy vector classes (Formula presented), 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.