83 citations · 1k across the 45 of their papers we have counts for
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Sharp approximations to the Bernoulli periodic functions by trigonometric polynomials
Emanuel Carneiro
We obtain optimal trigonometric polynomials of a given degree that majorize, minorize and approximate in the Bernoulli periodic functions. These ar…
Some extremal functions in Fourier analysis, III
Emanuel Carneiro, Jeffrey D. Vaaler
We obtain the best approximation in , by entire functions of exponential type, for a class of even functions that includes , where , and …
Some extremal functions in Fourier analysis, II
Emanuel Carneiro, Jeffrey D. Vaaler
We obtain extremal majorants and minorants of exponential type for a class of even functions on which includes and , where . We also give periodic…
On the regularity of maximal operators
Emanuel Carneiro, Diego Moreira
We study the regularity of the bilinear maximal operator when applied to Sobolev functions, proving that it maps $W^{1,p}(\mathbb{R}) \times W^{1,q}(\mathbb{R}) \to W^{1,r}(\mathbb…