Singular integrals on the complex affine group

Singular Integrals on Hilbert Space

exists as a bounded operator on L(H) as ô tends to zero and p tends to infinity. A theorem of this type extends the Calderon-Zygmund theory of singular integral operators on En to infinite dimensions. For if fc(#)||x||-" is a Calderon-Zygmund kernel and if £ is a bounded Borel set which is disjoint from a neighborhood of the origin then v{E) =fEk(x)\\x\\~ dx satisfies v(tE) = v(E) for £>0; if g...

Singular Integrals

In this paper I will a t tempt to describe the subject as it has developed in the last fifteen years, outlining the methods by which its problems have been approached and discussing its connections with other branches of Analysis. I t will perhaps be best to start by considering certain classical situations which lead naturally to singular integrals and which contain the seeds of some of the me...

p-ESTIMATES FOR SINGULAR INTEGRALS AND MAXIMAL OPERATORS ASSOCIATED WITH FLAT CURVES ON THE HEISENBERG GROUP

The maximal function along a curve (t, γ (t), tγ (t)) on the Heisenberg group is discussed. The L p-boundedness of this operator is shown under the doubling condition of γ ′ for convex γ in R. This condition also applies to the singular integrals when γ is extended as an even or odd function. The proof is based on angular LittlewoodPaley decompositions in the Heisenberg group.

Rough singular integrals on product spaces

where, p.v. denotes the principal value. It is known that if Φ is of finite type at 0 (see Definition 2.2) and Ω ∈ 1(Sn−1), then TΦ,Ω is bounded on Lp for 1<p <∞ [15]. Moreover, it is known that TΦ,Ω may fail to be bounded on Lp for any p if the finite-type condition is removed. In [8], Fan et al. showed that the Lp boundedness of the operator TΦ,Ω still holds if the condition Ω ∈ 1(Sn−1) is re...

Multi-parameter singular integrals