$L^p$ type mapping estimates for oscillatory integrals in higher dimensions

G. Sampson. "$L^{p}$ type mapping estimates for oscillatory integrals in higher dimensions." Studia Mathematica 172.2 (2006): 101-123. <http://eudml.org/doc/285278>.

@article{G2006,
abstract = {We show in two dimensions that if $Kf = ∫_\{ℝ₊²\} k(x,y)f(y)dy$, $k(x,y) = (e^\{ix^\{a\}·y^\{b\}\})/(|x-y|^\{η\})$, p = 4/(2+η), a ≥ b ≥ 1̅ = (1,1), $v_\{p\}(y) = y^\{(p/p^\{\prime \})(1̅-b/a)\}$, then $||Kf||_\{p\} ≤ C||f||_\{p,v_\{p\}\}$ if η + α₁ + α₂ < 2, $α_\{j\} = 1 - b_\{j\}/a_\{j\}$, j = 1,2. Our methods apply in all dimensions and also for more general kernels.},
author = {G. Sampson},
journal = {Studia Mathematica},
keywords = {oscillatory integrals; singular integrals; -boundedness},
language = {eng},
number = {2},
pages = {101-123},
title = {$L^\{p\}$ type mapping estimates for oscillatory integrals in higher dimensions},
url = {http://eudml.org/doc/285278},
volume = {172},
year = {2006},
}

TY - JOUR
AU - G. Sampson
TI - $L^{p}$ type mapping estimates for oscillatory integrals in higher dimensions
JO - Studia Mathematica
PY - 2006
VL - 172
IS - 2
SP - 101
EP - 123
AB - We show in two dimensions that if $Kf = ∫_{ℝ₊²} k(x,y)f(y)dy$, $k(x,y) = (e^{ix^{a}·y^{b}})/(|x-y|^{η})$, p = 4/(2+η), a ≥ b ≥ 1̅ = (1,1), $v_{p}(y) = y^{(p/p^{\prime })(1̅-b/a)}$, then $||Kf||_{p} ≤ C||f||_{p,v_{p}}$ if η + α₁ + α₂ < 2, $α_{j} = 1 - b_{j}/a_{j}$, j = 1,2. Our methods apply in all dimensions and also for more general kernels.
LA - eng
KW - oscillatory integrals; singular integrals; -boundedness
UR - http://eudml.org/doc/285278
ER -