Editing Potential theory (section)

==Spaces of harmonic functions==

Since the Laplace equation is linear, the set of harmonic functions defined on a given domain is, in fact, a [[vector space]]. By defining suitable [[normed vector space|norm]]s and/or [[inner product]]s, one can exhibit sets of harmonic functions which form [[Hilbert space|Hilbert]] or [[Banach space]]s. In this fashion, one obtains such spaces as the [[Hardy space]], [[Bloch space]], [[Bergman space]] and [[Sobolev space]].