Rodrigo Cardeccia

Fourier inequalities in variable Lebesgue spaces

We study the boundedness of the Fourier transform on variable Lebesgue spaces. We obtain necessary conditions and, independently, sufficient conditions on the exponents $p(\cdot)$ and $q(\cdot)$ under which the inequality $$\|\hat{f}\|_{q(\cdot)}\leq C\|f\|_{p(\cdot)}$$ holds for some constant $C>0$ and all $f\in L^{p(...