For 0 < q < and 0 < < , the tent space T q, () consists of all -measurable functions f such thatIn this note, we study the boundedness and compactness of the inclusion mapping i from Bergman-Morrey Spaces A p, to Tent Spaces T q, (

Let X and Y be two infinite dimensional Banach spaces and B(X ) (resp.B(Y ) ) be the algebra of bounded linear operators on X (resp.Y ).For T B(X ) and x X , T (x) denotes the local spectrum of T at x .Fix an integer k 2 , and let A 1 * A 2 * ... * A k stand for a generalized product of any k operators A 1 , A 2 , ... , A k B(X ) .Given two nonzero vectors x 0 X and y 0 Y , in this paper, we characterize all surjective maps : B(X ) B(Y ) which satisfy A 1 * A 2 * ... * A k (x 0 ) = (A 1 )

The weighted composition-differentiation operator of order n is denoted by D ,,n .In this paper, we investigate some basic properties of compact weighted composition-differentiation operators of order n on the Hardy space.Moreover, we obtain the upper estimate on the norm of the operator D ,,n , in the case that < 1 .