Weighted inequalities for holomorphic functional calculi of operators with heat kernel bounds

概要

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Let {\scrX} be a space of homogeneous type. Assume that L has a bounded holomorphic functional calculus on L^2(\varOmega) and L generates a semigroup with suitable upper bounds on its heat kernels where \varOmega is a measurable subset of {\scrX}. For appropriate bounded holomorphic functions b, we can define the operators b(L) on L^p({\varOmega}), 1≤ p≤ ∞. We establish conditions on positive weight functions u, v such that for each p, 1<p<∞, there exists a constant c_p such that ∈t_{\varOmega} |b(L)f(x)|^p u(x)dμ(x) ≤ c_p //b//^p<SUB>∞</SUB> ∈t_{\varOmega} |f(x)|^p v(x)dμ(x) for all f∈ L^p(vdμ). \\ ∈dentApplications include two-weight L^p inequalities for Schrödinger operators with non-negative potentials on \bm{R}^n and divergence form operators on irregular domains of \bm{R}^n.
社団法人日本数学会の論文
2005-10-01