If 
, then the Hardy space
is the class of functions holomorphic
on the disk 
and satisfying the growth condition
![||f||_(H^p)=sup_(0<r<1)[1/(2pi)int_0^(2pi)|f(re^(itheta))|^pdtheta]^(1/p)<infty,](/images/equations/HardySpace/NumberedEquation1.svg) |
where 
is the Hardy
norm.
Hardy Space
See also
Bergman Space, Hardy NormExplore with Wolfram|Alpha
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.Referenced on Wolfram|Alpha
Hardy SpaceCite this as:
Weisstein, Eric W. "Hardy Space." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/HardySpace.html