Harmonic Bergman Spaces

Throughout this chapter, p denotes a number satisfying 1 ≤ p < ∞. The Bergman space bp(Ω) is the set of harmonic functions u on Ω such that % MathType!MTEF!2!1!+- % feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 % qadaqbdaWdaeaapeGaamyDaaGaayzcSlaawQa7a8aadaWgaaWcbaWd % biaadchaa8aabeaak8qacqGH9aqpdaqadaWdaeaapeWaa8qea8aaba % Wdbmaaemaapaqaa8qacaWG1baacaGLhWUaayjcSdWdamaaCaaaleqa % baWdbiaadchaaaGccaWGKbGaamOvaaWcpaqaa8qacqqHPoWvaeqani % abgUIiYdaakiaawIcacaGLPaaapaWaaWbaaSqabeaapeGaaGymaiaa % c+cacaWGWbaaaOWdaiabgYda88qacqGHEisPaaa!4EE2! $${\left\| u \right\|_p} = {\left( {\int_\Omega {{{\left| u \right|}^p}dV} } \right)^{1/p}} < \infty $$ .