Some new Triebel-Lizorkin spaces on spaces of homogeneous type and their frame characterizations

Let（X,p,μ）d,θ be a space of homogeneous type,（?） ∈(0,θ],|s|＜（?） andmax{d/(d＋（?）),d/(d＋s＋（?）)}＜q≤∞.The author introduces the new Triebel-Lizorkin spaces （?）q（X） and establishes the framecharacterizations of these spaces by first establishing a Plancherel-P（?）lya-type inequalityrelated to the norm of the spaces （?）q（X）.The frame characterizations of the Besovspace （?）q（X） with|s|＜（?）,max{d/(d＋（?）),d/(d＋s＋（?）)}＜p≤∞ and 0＜q≤∞and the Triebel-Lizorkin space （?）q（X）with|s|＜（?）,max{d/(d＋（?）),d/(d＋s＋（?）)}＜p＜∞ and max{d/(d＋（?）),d/(d＋s＋（?）)}＜q≤∞ are also presented.Moreover,the au-thor introduces the new TriebeI-Lizorkin spaces b（?）q（X） and H（?）q（X） associated to agiven para-accretive function b.The relation between the space b（?）q（X） and the spaceH（?）q（X） is also presented.The author further proves that if s＝0 and q＝2,thenH（?）q（X）＝（?）q（X）,which also gives a new characterization of the space BMO（X）,since （?）q（X）＝BMO（X）.