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The Backward Shift On HP, William T. Ross
The Backward Shift On HP, William T. Ross
Department of Math & Statistics Faculty Publications
In this semi-expository paper, we examine the backward shift operator
Bf := (f-f(0)/z
on the classical Hardy space Hp. Through there are many aspects of this operator worthy of study [20], we will focus on the description of its invariant subspaces by which we mean the closed linear manifolds Ɛ ⊂ Hp for which BƐ ⊂ Ɛ. When 1 < p < ∞, a seminal paper of Douglas, Shapiro, and Shields [8] describes these invariant subspaces by using the important concept of a pseudocontinuation developed earlier by Shapiro [26]. When p = 1, the description is the same [1] except that in the proof, one must be mindful of some technical considerations involving the functions of bounded mean oscillation.