On the Fejér means of bounded Ciesielski systems
Copyright policy )On the Fejér means of bounded Ciesielski systems
Let \(\sigma^{(m,k)}_nf\) denote the Fejér means of the Ciesielski-Fourier series of \(f\), and let \(f^{(m,k)}_*(x)\) be the non-tangential maximal function of a tempered distribution \(f\). The main result states that: 1) \(\|\sigma^{(m,k)}_*f\|_{L^p}\leq C_p\|f\|_{H_p}\) for \(f\in H_p\) (Hardy space), \(\frac 12\varrho)\leq \frac c\varrho\|f\|_{L_1}\) for \(f\in L_1\).
Hardy spaces, atom, Summability and bases; functional analytic aspects of frames in Banach and Hilbert spaces, Fejér means, Ciesielski-Fourier series, Summability in several variables, interpolation, non-tangential maximal function, Spline approximation, spline systems, tempered distribution, atomic decomposition
Hardy spaces, atom, Summability and bases; functional analytic aspects of frames in Banach and Hilbert spaces, Fejér means, Ciesielski-Fourier series, Summability in several variables, interpolation, non-tangential maximal function, Spline approximation, spline systems, tempered distribution, atomic decomposition
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