Geodesic
New Inequalities in the Littlewood--Paley Theory and Estimates of the~$L_1$ Norm of Trigonometric Series and Polynomials
Informatics and Automation, Studies on function theory and differential equations, Tome 248 (2005), pp. 64-73

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Extensions of the Littlewood–Paley theorem to the limit values $p=1$ and $p=\infty$ are applied in order to obtain new lower bounds for the $L_1$ norms of trigonometric series and polynomials. Applications of the method to the estimation of polynomials with quadratic spectrum are suggested. 
@article{TRSPY_2005_248_a6,
     author = {S. V. Bochkarev},
     title = {New {Inequalities} in the {Littlewood--Paley} {Theory} and {Estimates} of the~$L_1$ {Norm} of {Trigonometric} {Series} and {Polynomials}},
     journal = {Informatics and Automation},
     pages = {64--73},
     publisher = {mathdoc},
     volume = {248},
     year = {2005},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2005_248_a6/}
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S. V. Bochkarev. New Inequalities in the Littlewood--Paley Theory and Estimates of the~$L_1$ Norm of Trigonometric Series and Polynomials. Informatics and Automation, Studies on function theory and differential equations, Tome 248 (2005), pp. 64-73. http://geodesic.mathdoc.fr/item/TRSPY_2005_248_a6/