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Sharp weak-type inequalities for Fourier multipliers and second-order Riesz transforms

100%

Osękowski A.

Open Mathematics

2014

tom 12

nr 8

1198-1213

We study sharp weak-type inequalities for a wide class of Fourier multipliers resulting from modulation of the jumps of Lévy processes. In particular, we obtain optimal estimates for second-order Riesz transforms, which lead to interesting a priori bounds for smooth functions on ℝd. The proofs rest on probabilistic methods: we deduce the above inequalities from the corresponding estimates for martingales. To obtain the lower bounds, we exploit the properties of laminates, important probability measures on the space of matrices of dimension 2×2, and some transference-type arguments.

Banach algebra of the Fourier multipliers on weighted Banach function spaces

75%

Karlovich A.

Concrete Operators

2015

tom 2

nr 1

Let MX,w(ℝ) denote the algebra of the Fourier multipliers on a separable weighted Banach function space X(ℝ,w).We prove that if the Cauchy singular integral operator S is bounded on X(ℝ, w), thenMX,w(ℝ) is continuously embedded into L∞(ℝ). An important consequence of the continuous embedding MX,w(ℝ) ⊂ L∞(ℝ) is that MX,w(ℝ) is a Banach algebra.

Ograniczanie wyników

1 Concrete Operators

1 Open Mathematics

1 Karlovich A.

1 Osękowski A.

1 2015

1 2014

Wyniki wyszukiwania

Sharp weak-type inequalities for Fourier multipliers and second-order Riesz transforms

Banach algebra of the Fourier multipliers on weighted Banach function spaces