Let B denote the Beurling–Ahlfors transform defined on Lp(C), 1 < p < ∞. The celebrated conjecture of T. Iwaniec states that its Lp norm ‖B‖p = p∗−1 where p∗ = max{p, p p−1}. In this paper the new… (More)

Let Xt be a Cauchy process in R , d ≥ 1. We investigate some of the fine spectral theoretic properties of the semigroup of this process killed upon leaving a domain D. We establish a connection… (More)

In this paper we study the behaviour in time of the trace (the partition function) of the heat semigroup associated with symmetric stable processes in domains of R. In particular, we show that for… (More)

This paper derives inequalities for multiple integrals from which sharp inequalities for ratios of heat kernels and integrals of heat kernels of certain Schrödinger operators follow. Such ratio… (More)

We study Fourier multipliers which result from modulating jumps of Lévy processes. Using the theory of martingale transforms we prove that these operators are bounded in L(R) for 1 < p < ∞ and we… (More)

We study the distribution of the exit place of iterated Brownian motion in a cone, obtaining information about the chance of the exit place having large magnitude. Along the way, we determine the… (More)

It is shown that the second term in the asymptotic expansion as t→ 0 of the trace of the semigroup of symmetric stable processes (fractional powers of the Laplacian) of order α, for any 0 < α < 2, in… (More)

The motivation for this paper comes from the following question on comparison of norms of conformal martingales X, Y in Rd, d ≥ 2. Suppose that Y is differentially subordinate to X. For 0 < p <∞,… (More)