Function spaces related to the Dirichlet space

@article{Arcozzi2011FunctionSR,
  title={Function spaces related to the Dirichlet space},
  author={Nicola Arcozzi and Richard Rochberg and Eric Sawyer and Brett D. Wick},
  journal={J. London Math. Society},
  year={2011},
  volume={83},
  pages={1-18}
}
H ·H := ̆ h = fg : f, g ∈ H ̄ = H ←↩ H is the product space of H2, by inner/outer factorization and Cauchy-Schwarz inequality. It is interesting, then, to find the dual space of H1. C. Fefferman [7] proved that, under the H2 paring (with some care), (H2 ·H2)∗ = (H1)∗ = BMO∩H(D) is the space of the analytic functions with bounded mean oscillation. The definition of BMO, born out of a problem in elasticity theory [9], in our context is as follows. A complex valued function b on the torus T has… CONTINUE READING

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