Convolution Calderón-Zygmund singular integral operators with rough kernels

Abstract

A survey of known results in the theory of convolution type Calderón-Zygmund singular integral operators with rough kernels is given. Some recent progress is discussed. A list of remaining open questions is presented.

LpBOUNDS FOR THE PARABOLIC LITTLEWOOD-PALEY OPERATOR ASSOCIATED TO SURFACES OF REVOLUTION

“…and Ω satisfies a condition introduced by Grafakos and Stefanov in [6]. The result in the paper extends some known results.…”

“…In this paper the authors study the L p boundedness for parabolic Littlewood-Paley operatorwhereand Ω satisfies a condition introduced by Grafakos and Stefanov in [6]. The result in the paper extends some known results.…”

“…Condition (1.3) was introduced by Grafakos and Stefanov in [6]. The examples in [6] show that there is the following relationship between F β (S n−1 ) and…”

L p Bounds for the parabolic singular integral operator

“…For each j, we define Φ j in ℝ n by 8) and let δ represent the Dirac delta on ℝ, then by (2.7), for any Schwartz function f,…”

“…Condition (1.3) was introduced by Grafakos and Stefanov [8]. The examples in [8] show that there is the following relationship between F b (S n-1 ) and…”