On $L_p-L_q$ boundedness for convolutions with kernels having singularities on a sphere

Alexey N. Karapetyants. "On $L_{p} - L_{q}$ boundedness for convolutions with kernels having singularities on a sphere." Studia Mathematica 144.2 (2001): 121-134. <http://eudml.org/doc/286126>.

@article{AlexeyN2001,
abstract = {For the convolution operators $A_\{a\}^\{α\}$ with symbols $a(|ξ|)|ξ|^\{-α\} exp\{i|ξ|\}$, 0 ≤ Re α < n, $a(|ξ|) ∈ L_\{∞\}$, we construct integral representations and give the exact description of the set of pairs (1/p,1/q) for which the operators are bounded from $L_\{p\}$ to $L_\{q\}$.},
author = {Alexey N. Karapetyants},
journal = {Studia Mathematica},
keywords = {convolution; multiplier; singular integral; space},
language = {eng},
number = {2},
pages = {121-134},
title = {On $L_\{p\} - L_\{q\}$ boundedness for convolutions with kernels having singularities on a sphere},
url = {http://eudml.org/doc/286126},
volume = {144},
year = {2001},
}

TY - JOUR
AU - Alexey N. Karapetyants
TI - On $L_{p} - L_{q}$ boundedness for convolutions with kernels having singularities on a sphere
JO - Studia Mathematica
PY - 2001
VL - 144
IS - 2
SP - 121
EP - 134
AB - For the convolution operators $A_{a}^{α}$ with symbols $a(|ξ|)|ξ|^{-α} exp{i|ξ|}$, 0 ≤ Re α < n, $a(|ξ|) ∈ L_{∞}$, we construct integral representations and give the exact description of the set of pairs (1/p,1/q) for which the operators are bounded from $L_{p}$ to $L_{q}$.
LA - eng
KW - convolution; multiplier; singular integral; space
UR - http://eudml.org/doc/286126
ER -