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- W4386050433 abstract "One of the main goals in this chapter is to estimate singular integral operators of “chord-dot-normal” type, associated with Ahlfors regular domains $$Omega subseteq {mathbb {R}}^n$$ with unbounded boundaries, in a manner which makes it clear how the flatness of said domains affects the size of these operators on various function spaces. A fitting way to quantify flatness in this setting is via the BMO semi-norm of the geometric measure theoretic outward unit normal $$nu $$ to $$Omega $$ . The reason we shall focus on singular integral operators of “chord-dot-normal” type is that they are sensitive to flatness, in the sense that they all become identically zero when the underlying domain $$Omega $$ is a half-space in $${mathbb {R}}^n$$ . By way of contrast, SIO’s like the Cauchy singular integral operator do not. In summary, there are much better estimates for singular integral operators of “chord-dot-normal” type on the boundaries of UR domains than for generic convolution type singular integral operators. Ultimately, our work here solidifies the connections between the regularity of a domain (measured in terms of the mean oscillations of its geometric measure theoretic outward unit normal) on the one hand, and singular integrals and boundary value problems for elliptic partial differential equations considered in said domain, on the other hand." @default.
- W4386050433 created "2023-08-23" @default.
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- W4386050433 date "2023-01-01" @default.
- W4386050433 modified "2023-09-25" @default.
- W4386050433 title "Norm Estimates and Invertibility Results for SIO’s on Unbounded Boundaries" @default.
- W4386050433 doi "https://doi.org/10.1007/978-3-031-31561-9_4" @default.
- W4386050433 hasPublicationYear "2023" @default.
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