Stummel class of Morrey spaces
Let \[ \mathcal{M}_{1,\varphi}=\left\{f\in L^1_{\text{loc}}(\mathbb{R}^n)\,\biggl|\, \sup_B \frac{1}{\varphi(B)}\int_B|f(y)|\,dy <\infty\right\} \] be the generalized Morrey space, where \(\psi: (0,\infty ) \to (0,\infty)\) satisfies the doubling condition. The authors study relations between the space \(\mathcal{M}_{1,\varphi}\) and the class \[ S_\psi = \left\{f\in L^p_{\text{loc}}(\mathbb{R}^n)\,\Bigl|\, \lim_{r\to 0} \psi_f(r)\right\}, \quad \psi_f(r) = \sup_{x\in\mathbb{R}^n}\int_{|x-y|<r} |f(y)| \frac{\psi(|x-y|)}{|x-y|^n}\,dy . \]
scientific article; zbMATH DE number 5077520