Ajay K. Sharma
Abstract
Abstract We investigate compact composition operators acting on generalized Hardy spaces 𝐻𝑤. In fact, we prove that if 𝑤 is a differentiable, subharmonic and strictly increasing function defined on [0, ∞), then 𝐶 φ is compact on the generalized Hardy spaces if and only if it is compact on the Hardy space 𝐻2.
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Abstract We investigate compact composition operators acting on generalized Hardy spaces 𝐻𝑤. In fact, we prove that if 𝑤 is a differentiable, subharmonic and strictly increasing function defined on [0, ∞), then 𝐶 φ is compact on the generalized Hardy spaces if and only if it is compact on the Hardy space 𝐻2.
Key concepts: Hardy space, Mathematics, Pure mathematics, Composition (language), Differentiable function, Compact operator on Hilbert space, Space (punctuation), Compact space