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

作者：Duong, XT^*; Yan, LX

来源：Journal of the Mathematical Society of Japan, 2005, 57(4): 1129-1152.

DOI：10.2969/jmsj/1150287306

• holomorphic functional calculus
• space of homogeneous type
• singular integral operator
• weights
• semigroup kernel
• elliptic operator

Let X be a space of homogeneous type. Assume that L has a bounded holomorphic functional calculus on L-2(Omega) and L generates a semigroup with suitable upper bounds on its heat kernels where Omega is a measurable subset of X. For appropriate bounded holomorphic functions b, we can define the operators b(L) on L-p (Omega), 1 <= p <= infinity. We establish conditions on positive weight functions u, v such that for each p, 1 < p < infinity, there exists a constant c(p) such that
integral(Omega)vertical bar b(L)f(x)vertical bar(p)u(x)d mu(x) <= c(p)parallel to b parallel to(infinity)(p) integral(Omega)vertical bar(x)vertical bar(p)v(x)d mu(x)
for all f is an element of L-p(vd mu).
Applications include two-weight LP inequalities for Schrodinger operators with non-negative potentials on R-n and divergence form operators on irregular domains of R-n.

• 出版日期2005-10
• 单位中山大学