For 1≤p<∞we introduce a notion of"p-mean oscillation"on C^(n)in terms of the q metric induced by reproducing kernel of F_(ψ)^(2).It is shown that the densely-defined Hankel operators Hf,Hf:F_(ψ)^(p)→...For 1≤p<∞we introduce a notion of"p-mean oscillation"on C^(n)in terms of the q metric induced by reproducing kernel of F_(ψ)^(2).It is shown that the densely-defined Hankel operators Hf,Hf:F_(ψ)^(p)→F_(ψ)^(p),are simultaneously bounded if and only if f is of bounded“p-mean oscillation”.Furthermore,it is also shown that the densely-defined Hankel operators Hf、Hf:F_(ψ)^(p)→F_(ψ)^(p),are simultaneously compact if and only if f is of vanishing“p-mean oscillation”.Here the weightψis a positive function of logarithmic grow th sat isfying certain suitable conditions.展开更多
文摘For 1≤p<∞we introduce a notion of"p-mean oscillation"on C^(n)in terms of the q metric induced by reproducing kernel of F_(ψ)^(2).It is shown that the densely-defined Hankel operators Hf,Hf:F_(ψ)^(p)→F_(ψ)^(p),are simultaneously bounded if and only if f is of bounded“p-mean oscillation”.Furthermore,it is also shown that the densely-defined Hankel operators Hf、Hf:F_(ψ)^(p)→F_(ψ)^(p),are simultaneously compact if and only if f is of vanishing“p-mean oscillation”.Here the weightψis a positive function of logarithmic grow th sat isfying certain suitable conditions.
