Interpolation between Some Banach Spaces in Generalized Harmonic Analysis: The Real Method
Interpolation between Some Banach Spaces in Generalized Harmonic Analysis: The Real Method
In [3], A. Beurling introduced the space $A^{p}(R$ ' $)$ , $ 1<p<\infty$ , as $A^{p}(R^{1})=\{f$ : $\Vert f\Vert_{A^{p}\langle R^{1})}=\inf_{\omega e\Omega}(\int_{-\infty}^{\infty}|f(x)|^{p}\omega(x)^{-(p-1)}dx)^{1/p}<\infty\}$ , where $\Omega$ is the class of functions $\omega$ on $R^{1}$ such that $\omega$ is positive, even, nonincreasing with respect to $|x|$ , and $\omega(0)+\int_{-\infty}^{\infty}\omega(x)dx=1$ .By regarding $A^{p}(R^{1})$ as …