On the convergence of parabolically scaled two-dimensional Fourier series in the linear phase setting
Studia Mathematica, Tome 237 (2017) no. 2, pp. 101-117
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
For $$Sf(x,y)=\int ^\pi _{-\pi }\int ^\pi _{-\pi } {{e^{iM^2(x,y) y’}}\over {y’} }\, {{e^{iM(x,y) x’}}\over {x’}}f(x-x’,y-y’)\, dx’\, dy’ ,$$ the linearized maximal operator of the rectangular partial sums of the kind $(M,M^2)$ for double Fourier series, we prove a weak-type $(L^r, L^{r-\varepsilon })$ estimate for $1 \lt r\leq 2$ and any $\varepsilon \gt 0$ in case $M^2(x,y)=Ax+By$ with $x,y \in [0,2\pi ],$ uniformly with respect to $A, B\geq 0.$
Keywords:
int int x x y y linearized maximal operator rectangular partial sums kind double fourier series prove weak type r varepsilon estimate leq varepsilon uniformly respect geq
Affiliations des auteurs :
Elena Prestini 1
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author = {Elena Prestini},
title = {On the convergence of parabolically scaled two-dimensional {Fourier} series in the linear phase setting},
journal = {Studia Mathematica},
pages = {101--117},
publisher = {mathdoc},
volume = {237},
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year = {2017},
doi = {10.4064/sm8182-10-2016},
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Elena Prestini. On the convergence of parabolically scaled two-dimensional Fourier series in the linear phase setting. Studia Mathematica, Tome 237 (2017) no. 2, pp. 101-117. doi: 10.4064/sm8182-10-2016
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