For the domains of the space Rn, n≥2, with a finite number of conical points, one proves embedding theorems for the spaces of harmonic functions which generalize the Littlewood-Paley and Carleson theorems. Let ∥·∥p, Ω be a norm which is transferred in some natural manner to the space of harmonic functions in the domain Ω and which in the unit circle of the space ℝ2 turns into the norm of the Hardy space Hp and let ℋp(Ω) be the space of harmonic functions in Ω with this norm. One establishes, in particular, sufficient conditions on the measure V, for which one has the inequality[Figure not available: see fulltext.].
Original language | English |
---|---|
Pages (from-to) | 1173-1176 |
Number of pages | 4 |
Journal | Journal of Soviet Mathematics |
Volume | 14 |
Issue number | 2 |
DOIs | |
State | Published - Aug 1980 |
Externally published | Yes |
ID: 86666826