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- W2912497959 abstract "Let $0<unicode[STIX]{x1D6FC}<n,1leq p<q<infty$ with $1/p-1/q=unicode[STIX]{x1D6FC}/n$ , $unicode[STIX]{x1D714}in A_{p,q}$ , $unicode[STIX]{x1D708}in A_{infty }$ and let $f$ be a locally integrable function. In this paper, it is proved that $f$ is in bounded mean oscillation $mathit{BMO}$ space if and only if $$begin{eqnarray}sup _{B}frac{|B|^{unicode[STIX]{x1D6FC}/n}}{unicode[STIX]{x1D714}^{p}(B)^{1/p}}bigg(int _{B}|f(x)-f_{unicode[STIX]{x1D708},B}|^{q}unicode[STIX]{x1D714}(x)^{q},dxbigg)^{1/q}<infty ,end{eqnarray}$$ where $unicode[STIX]{x1D714}^{p}(B)=int _{B}unicode[STIX]{x1D714}(x)^{p},dx$ and $f_{unicode[STIX]{x1D708},B}=(1/unicode[STIX]{x1D708}(B))int _{B}f(y)unicode[STIX]{x1D708}(y),dy$ . We also show that $f$ belongs to Lipschitz space $Lip_{unicode[STIX]{x1D6FC}}$ if and only if $$begin{eqnarray}sup _{B}frac{1}{unicode[STIX]{x1D714}^{p}(B)^{1/p}}bigg(int _{B}|f(x)-f_{unicode[STIX]{x1D708},B}|^{q}unicode[STIX]{x1D714}(x)^{q},dxbigg)^{1/q}<infty .end{eqnarray}$$ As applications, we characterize these spaces by the boundedness of commutators of some operators on weighted Lebesgue spaces." @default.
- W2912497959 created "2019-02-21" @default.
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- W2912497959 date "2019-01-30" @default.
- W2912497959 modified "2023-10-16" @default.
- W2912497959 title "CHARACTERIZATIONS OF BMO AND LIPSCHITZ SPACES IN TERMS OF WEIGHTS AND THEIR APPLICATIONS" @default.
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- W2912497959 doi "https://doi.org/10.1017/s1446788718000447" @default.
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