AA
Alex Amenta
Authored
5 records found
LpLq Off-diagonal estimates for the Ornstein-Uhlenbeck semigroup
Some positive and negative results
We investigate Lp(γ)-Lq(γ) off-diagonal estimates for the Ornstein-Uhlenbeck semigroup (etL)t>0. For sufficiently large t (quantified in terms of p and q), these estimates hold in an unrestricted sense, while, for sufficiently small t, they fail when restricted to maximal admissi
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We extend Rubio de Francia's extrapolation theorem for functions valued in UMD Banach function spaces, leading to short proofs of some new and known results. In particular we prove Littlewood-Paley-Rubio de Francia-type estimates and boundedness of variational Carleson operators
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Given a metric measure space X, we consider a scale of function spaces (Formula presented.), called the weighted tent space scale. This is an extension of the tent space scale of Coifman, Meyer, and Stein. Under various geometric assumptions on X we identify some associated inter
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Given a sequence of complete Riemannian manifolds (Mn) of the same dimension, we construct a complete Riemannian manifold M such that for all p ∈(1,∞) the Lp-norm of the Riesz transform on M dominates the Lpnorm of the Riesz transform on Mn for all n. Thus we establish the follow
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Contributed
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In this bachelor's thesis we will solve the Dirichlet problem with an Lp(T) boundary function. First, we will focus on the holomorphic version of the Dirichlet problem and introduce Hardy space theory, from which will follow a sufficient condition on the Fourier coefficients of t
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