A WEAK-(p, q) INEQUALITY FOR FRACTIONAL INTEGRAL OPERATOR ON MORREY SPACES OVER METRIC MEASURE SPACES

Abstract

This paper presents a weak-(p, q) inequality for fractional integral operator on Morrey spaces over metric measure spaces of nonhomogeneous type. Both parameters p and q are greater than or equal to one. The weak-(p, q) inequality is proved by employing an inequality involving maximal operator on the spaces under consideration.

Characterization of the boundedness of generalized fractional integral and maximal operators on Orlicz–Morrey and weak Orlicz–Morrey spaces

“…For their generalization, see, for example, [33, 36, 48, 49]. Weak Morrey spaces were studied in , for example,[13, 14, 53, 58, 63]. The Orlicz–Morrey space $$L^{(\Phi ,\varphi )}(\mathbb {R}^n)$$ was first studied in [41].…”

Weak‐type Fefferman–Stein inequality and commutators on weak Orlicz–Morrey spaces

“…For their generalization, see [38,42,57,58], etc. Weak Morrey spaces were studied in [16,17,62,70,76], etc. The Orlicz-Morrey space 𝐿 (Φ,𝜑) (ℝ 𝑛 ) was first studied in [47].…”

“…For their generalization, see [38, 42, 57, 58], etc. Weak Morrey spaces were studied in [16, 17, 62, 70, 76], etc. The Orlicz–Morrey space $$L^{(\Phi ,\varphi )}(\mathbb {R}^n)$$ was first studied in [47].…”