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Kato's conjecture is a mathematical problem named after mathematician Tosio Kato, of the University of California, Berkeley. Kato initially posed the problem in 1953. Kato asked whether the square roots of certain elliptic operators, defined via functional calculus, are analytic. The full statement of the conjecture as given by Auscher et al. is: "the domain of the square root of a uniformly complex elliptic operator with bounded measurable coefficients in Rn is the Sobolev space H1(Rn) in any dimension with the estimate ".

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  • Kato's conjecture (en)
  • 加藤予想 (ja)
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  • 加藤予想（かとうよそう、英: Kato's conjecture）は、楕円型作用素の平方根が解析的かを問う数学上の問題である。名称は提案者である数学者の加藤敏夫に因む。加藤予想は1953年に加藤によって提案された。Pascal Auscher、スティーヴ・ホーフマン、マイケル・レイシー、アラン・マッキントッシュとPhilippe Tchamitchianによって2001年に共同で解決されるまで、問題はほぼ半世紀の間未解決のままだった。 (ja)
  • Kato's conjecture is a mathematical problem named after mathematician Tosio Kato, of the University of California, Berkeley. Kato initially posed the problem in 1953. Kato asked whether the square roots of certain elliptic operators, defined via functional calculus, are analytic. The full statement of the conjecture as given by Auscher et al. is: "the domain of the square root of a uniformly complex elliptic operator with bounded measurable coefficients in Rn is the Sobolev space H1(Rn) in any dimension with the estimate ". (en)
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  • Kato's conjecture is a mathematical problem named after mathematician Tosio Kato, of the University of California, Berkeley. Kato initially posed the problem in 1953. Kato asked whether the square roots of certain elliptic operators, defined via functional calculus, are analytic. The full statement of the conjecture as given by Auscher et al. is: "the domain of the square root of a uniformly complex elliptic operator with bounded measurable coefficients in Rn is the Sobolev space H1(Rn) in any dimension with the estimate ". The problem remained unresolved for nearly a half-century, until in 2001 it was jointly solved in the affirmative by Pascal Auscher, Steve Hofmann, Michael Lacey, Alan McIntosh, and . (en)
  • 加藤予想（かとうよそう、英: Kato's conjecture）は、楕円型作用素の平方根が解析的かを問う数学上の問題である。名称は提案者である数学者の加藤敏夫に因む。加藤予想は1953年に加藤によって提案された。Pascal Auscher、スティーヴ・ホーフマン、マイケル・レイシー、アラン・マッキントッシュとPhilippe Tchamitchianによって2001年に共同で解決されるまで、問題はほぼ半世紀の間未解決のままだった。 (ja)
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