Necessary conditions for the $L^{p}$-convergence $(0<p<1)$ of single and double trigonometric series

We give necessary conditions in terms of the coefficients for the convergence of a double trigonometric series in the $L^{p}$-metric, where $0Hardy-Littlewood inequality for functions in $H^{p}$ and the Bernstein-Zygmund inequalities for the derivatives of trigonometric polynomials and their conjugates in the $L^{p}$-metric, where $0

Keywords:

• Mathematical proof
• Convergence (routing)
• Conjugate
• Mathematical analysis
• Trigonometric series
• Trigonometry
• Inequality
• Mathematics
• Polynomial
• Discrete mathematics

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