In this paper we study some boundary operators of a class of Bessel-type Littlewood-Paley extensions whose prototype is ?xu(x, y) + 1 - 2s?u?y (x, y) + ??y2u2 (x, y) = 0 for x ? Rd, y > 0, y u(x, 0) = f(x) for x ? Rd. In particular, we show that with a logarithmic scaling one can capture the failure of analyticity of these extensions in the limiting cases s = k ? N.
|Number of pages||17|
|Journal||Discrete and Continuous Dynamical Systems - Series S|
|State||Published - 1 Jun 2018|
- Bessel functions
- Boundary operator
- Functional calculus
- Littlewood-Paley extension