Smooth pointwise multipliers of modulation spaces

Smooth pointwise multipliers of modulation spaces

Let 1 < p, q < ∞ and s, r ∈ R. It is proved that any function in the amalgam space W (H p′(R ), l∞), where p ′ is the conjugate exponent to p and H p′(R ) is the Bessel potential space, defines a bounded pointwise multiplication operator in the modulation space M p,q(R ), whenever r > |s|+ d.

Non-smooth atomic decompositions, traces on Lipschitz domains, and pointwise multipliers in function spaces

We provide non-smooth atomic decompositions for Besov spaces Bsp,q(R n), s > 0, 0 < p, q ≤ ∞, defined via differences. The results are used to compute the trace of Besov spaces on the boundary Γ of bounded Lipschitz domains Ω with smoothness s restricted to 0 < s < 1 and no further restrictions on the parameters p, q. We conclude with some more applications in terms of pointwise multipliers. Ma...

POINTWISE MULTIPLIERS FOR REVERSE HÖLDER SPACES II By

We classify weights which map strong reverse Hölder weight classes to weak reverse Hölder weight spaces under pointwise multiplication.

Pointwise Multipliers of Besov Spaces of Smoothness Zero and Spaces of Continuous Functions

A Class of Fourier Multipliers for Modulation Spaces

We prove the boundedness of a general class of Fourier multipliers, in particular of the Hilbert transform, on modulation spaces. In general, however, the Fourier multipliers in this class fail to be bounded on L spaces. The main tools are Gabor frames and methods from time-frequency analysis.