Estimates of the Besov norm on a bounded fractal lateral boundary and the boundedness of operators

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Consider a cylindrical domain Ω_D=D×(0, T), where D is a bounded domain with fractal boundary in R^d. Let μ be a λ-Holder continuous function on Ω_D with respect to the parabolic metric ρ. We estimate the Besov norm of the restriction of μ to S_D=∂D×[0, T] by the L^p(Ω_D)-norm of the sum of |▽_yμ(Y)|dist(Y, S_D)^<λ_1> and |D_<d+1>μ(Y)|dist(Y, S_D)^<λ_2> for suitable λ_1 and λ_2. We apply it to show the boundedness of an operator on the Besov space on S_D and use the result to prove the boundedness of the operator with respect to the double layer heat potentials. 2000 Mathematics Subject Classification : Primary 46E35, 31B15

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