In this paper, we first consider boundedness properties of a family of operators generalizing the Hilbert operator in the upper triangle case. In the diagonal case, we give the exact norm of these operators under some restrictions on the parameters. We secondly consider boundedness properties of a family of positive Bergman-type operators of the upper-half plane. We give necessary and sufficient conditions on the parameters under which these operators are bounded in the upper triangle case.2010 Mathematics Subject Classification. Primary 47B34, 26D15; Secondary 28A25.
We consider two families of multilinear Hilbert-type operators for which we give exact relations between the parameters so that they are bounded. We also find the exact norm of these operators.
We discuss martingale transforms between martingale Hardy-amalgam spaces H p , q s , Q p , q and P p , q . Let 0 < p < q < ∞ , p 1 < p and q 1 < q and let f = f n , n ∈ ℕ be a martingale in P p 1 , q 1 ; then, we show that its martingale transforms are the martingales in P p , q for some p , q and similarly for H p , q s and Q p , q .
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