Interpolation for weak Orlicz spaces with M Δ condition

Abstract

An interpolation theorem for weak Orlicz spaces generalized by N-functions satisfying MΔ condition is given. It is proved to be true for weak Orlicz martingale spaces by weak atomic decomposition of weak Hardy martingale spaces. And applying the interpolation theorem, we obtain some embedding relationships among weak Orlicz martingale spaces.

Weak Orlicz–Hardy martingale spaces

“…The main goal of this present paper is to deal with the weak Orlicz-Hardy martingale spaces, which are more inclusive classes than Orlicz-Hardy martingale spaces, and give the weak version of Miyamoto, Nakai and Sadasue's results. In 2008 the weak Orlicz spaces and weak Orlicz-Hardy martingale spaces generated by nice young functions satisfying the M △ -condition were first introduced in [5], and interpolation theorems and inequalities were proved for these spaces; Liu et al investigated the boundedness of some sublinear operators defined on weak Orlicz-Hardy martingale spaces in [9] and the first named author studied some embedding relationships between them in [7] in 2011; however, the existing results about weak Orlicz-Hardy martingale spaces are all associated with convex functions. In the present paper we are interested in the case Φ is not convex.…”

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

“…For the theory of Orlicz spaces, see [25, 26, 28, 32, 51] for example. Weak Orlicz spaces were studied in, for example, [21, 31, 40]. Morrey spaces were introduced by [35].…”

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

“…For the theory of Orlicz spaces, see [30, 31, 34, 37, 60], for example. Weak Orlicz spaces were studied in [26, 46], etc. Morrey spaces were introduced by [41].…”