<i><i>h</i><sub>p</sub>(X</i>) class of<i> X</i>-valued harmonic functions and applications

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Bılalov B., Sadigova S. R., Sezer Y., Ildiz U., Buyukarslan A.

FILOMAT, vol.39, no.35, pp.12593-12609, 2025 (SCI-Expanded, Scopus) identifier identifier

  • Publication Type: Article / Article
  • Volume: 39 Issue: 35
  • Publication Date: 2025
  • Doi Number: 10.2298/fil2535593b
  • Journal Name: FILOMAT
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH
  • Page Numbers: pp.12593-12609
  • Open Archive Collection: AVESIS Open Access Collection
  • Yıldız Technical University Affiliated: Yes

Abstract

The concept of t-basis (generated by the tensor product) from the exponential system E = {e(int)}(n is an element of Z) is considered for Bochner space L-p(I-0; X), 1 < p < +infinity, on I-0 = [-pi, pi), where X is a Banach space with UMD (Unconditional Martingale Difference) property. We assume that Xis endowed with the involution (*). Using the t-basicity of the system epsilon, we introduce the class h(p)(+;R) of X-valued harmonic functions in the unit ball, generated by involution (*). The *-analogues of the Cauchy-Riemann conditions are obtained, and the relations between the class h(p)(+;R) (X) and the Hardy-Bochner class H-p(X) of analytic functions are established. A new method for establishing X-valued Sokhotski-Plemelj's formulas is presented. Additionally, we establish the correctness of the Dirichlet problem for X-valued harmonic functions in the class h(p)(X).