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Hardy Space


If 0<p<infty, then the Hardy space H^p(D) is the class of functions holomorphic on the disk D and satisfying the growth condition

 ||f||_(H^p)=sup_(0<r<1)[1/(2pi)int_0^(2pi)|f(re^(itheta))|^pdtheta]^(1/p)<infty,

where ||f||_(H^p) is the Hardy norm.


See also

Bergman Space, Hardy Norm

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References

Duren, P. L. Theory of H-p Spaces. New York: Academic Press, 1970.Garnett, J. Bounded Analytic Functions. New York: Academic Press, 1981.Koosis, P. Introduction to H-p Spaces, 2nd ed. Cambridge, England: Cambridge University Press, 1998.Krantz, S. G. "Hardy Spaces." §12.3 in Handbook of Complex Variables. Boston, MA: Birkhäuser, pp. 152-154, 1999.

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Hardy Space

Cite this as:

Weisstein, Eric W. "Hardy Space." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/HardySpace.html

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