Fractional maximal operator in Orlicz spaces

Fractional Integration in Orlicz Spaces

Fractional integration and convolution results are given for Orlicz spaces using an inequality earlier developed for Aa(X~) spaces which generalize Lorentz L(p,q) spaces. The extension problem for convolution operators encountered previously by other authors is almost entirely avoided.

Orlicz-Garling sequence spaces of difference operator and their domination in Orlicz-Lorentz spaces

We introduce new classes of generalized Orlicz-Garling sequences and Orlicz-Lorentz sequences by using a sequence of Orlicz functions and difference operator. We show that the Orlicz-Garling sequence space admits a unique 1-subsymmetric basis and a 1-dominated block basic sequence in [Formula: see text]. We also make an effort to prove that every symmetric normalized block Orlicz-Garling sequen...

Orlicz Spaces for Which the Hardy-littlewood Maximal Operator Is Bounded

Subspaces of Maximal Operator Spaces

A Banach space E can be embedded into B(H) in a variety of ways. The embeddings giving rise to the minimal and maximal possible operator space norms (introduced in [1], [3] and [4] and further investigated in [21] and [22]) are especially interesting to us. Let A be the set of all functionals on E of norm not exceeding 1 and let B be the set of all linear maps T : E → Mn such that ||T || ≤ 1 (h...

Two-Weight Orlicz Type Integral Inequalities for the Maximal Operator

p A v = u  , (1) holds for t = ) t ( = ) t (   , but not if 1 = p . Also for each   < p 1 there exists a pair p A ) v , u (  so that (1) fails in the special case t = ) t ( = ) t (   [3, p. 395]. In these exceptional cases we have a weak type inequality. An excellent reference is the book by J.Garcia-Cuerva and J.L.Rubio de Francia [3]. We refer the reader interested in the current stat...