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In this paper, we give a new definition of a class of quaternion function spaces, which will be called $$F(p,\alpha ,s;E)$$F(p,α,s;E)-type spaces. Then, we characterize quaternion $$\alpha $$α-Bloch functions by… Click to show full abstract
In this paper, we give a new definition of a class of quaternion function spaces, which will be called $$F(p,\alpha ,s;E)$$F(p,α,s;E)-type spaces. Then, we characterize quaternion $$\alpha $$α-Bloch functions by functions belonging to $$F(p,\alpha ,s;E)$$F(p,α,s;E) spaces under some mild conditions on the weighted function E. Besides, we give some essential properties for the extended little $$\alpha $$α-Bloch spaces. Further, we study extreme points on the unit ball of some quaternion function spaces such that the spaces $$F(p,\alpha ,s;E).$$F(p,α,s;E).
Journal Title: Advances in Applied Clifford Algebras
Year Published: 2018
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