Some Generalized Hardy Spaces |
Common terms and phrases
A-element a.e. x e G abelian group absolutely continuous analytic and harmonic analytic functions archimedean Banach algebra Banach space Borel function Borel measure Borel sets Borel subset boundary values Chapter completes the proof continuous function convergence Corollary defined on G Definition denote dual groups f is harmonic f|Pam finite regular Borel Fn(a Fourier transform Fourier-Stieltjes transform Fubini theorem function f function on G functions defined group G groups whose dual h in LP(G Haar measure Haar measure zero half-plane Hardy spaces harmonic functions harmonic polynomials hence Hom(S,E homomorphism isometrically isomorphic JCP(A Karel deLeeuw Lš(A Lš(G Let f linearly ordered LP G LP(A mapping measure on G non-negative p-integrable Proposition prove quasi-harmonic functions real numbers regular Borel measure representing function resp respect to Haar satisfies semigroup of type shows space HP(A topology unique unit disk