Polynomial Approximation by Doubly Periodic Weierstrass Functions on Disjoint Segments in the LP Metric

Let sk, 1 ≤ k ≤ m, m ≥ 2, be disjoint segments lying in a parallelogram Q. Denote by ℘(z) a doubly periodic Weierstrass function with the fundamental parallelogram Q. Let fk : sk → ℂ be functions, and let fk′\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${f}_{k}^{\prime}$$\end{document} ∈ Lpk\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${L}^{{p}_{k}}$$\end{document} (sk), 1 ≤ k ≤ m, 1 < pk < ∞.