Absolutely summing multipliers on abstract Hardy spaces

Norm estimates for matrix operators between Banach spaces

“…In consequence, from the result of Xu (see [26], cf. [19]), it follows that HX is an interpolation space between H p and H q . Since the system {u n } forms a basis in H p for any 1 < p < ∞, the operators S n are uniformly bounded in both H p and H q (see [12,Section 2.3]).…”

“…Notice that for every exact interpolation functor F (F( 2 , 1 ), HF(L 2 (T), L ∞ (T))) forms a Hausdorff-Young pair with constant C = 1 (see [19]). Now, if φ ∈ U, and F := φ u is the upper Ovchinnikov functor, then for every couple (X 0 , X 1 ) of maximal Banach lattices on ( , μ), we have (see [22]) F(X 0 , X 1 ) = φ(X 0 , X 1 ).…”

“…Motivated by the Hausdorff-Young inequalities, in [19] we introduced the notion of HausdorffYoung pairs. Let X be an r.i. space on T and let E and G be Banach sequence lattices on Z + .…”

Carleson measures and embeddings of abstract Hardy spaces into function lattices

“…It is well known from the classical theory of H p -spaces that f ∈ N + belongs to H p if and only if the radial limit f ∈ L p (m) and f H p = f L p (m) (see, e.g., [5,6]). In the sequel we use the following fact without any references: if X is a symmetric space on T, then f ∈ HX implies f ∈ X ×× and f HX = f X ×× (see [11,Proposition 2.2]). In fact, we have HX = {f ∈ HX ; f ∈ X}.…”

Compact multipliers on spaces of analytic functions

“…It's worth mentioning that p-summing multipliers were studied in the context of H p spaces (see [1]) and in reference to abstract Hardy spaces (see [13]). …”