Displaying similar documents to “On the boundedness of the mapping f → | f | in Besov spaces”

The scalar Oseen operator - Δ + ∂ / ∂ x 1 in ℝ 2

Chérif Amrouche, Hamid Bouzit (2008)

Applications of Mathematics

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This paper solves the scalar Oseen equation, a linearized form of the Navier-Stokes equation. Because the fundamental solution has anisotropic properties, the problem is set in a Sobolev space with isotropic and anisotropic weights. We establish some existence results and regularities in L p theory.

On some structural properties of Banach function spaces and boundedness of certain integral operators

T. S. Kopaliani (2004)

Czechoslovak Mathematical Journal

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In this paper the notions of uniformly upper and uniformly lower ℓ -estimates for Banach function spaces are introduced. Further, the pair ( X , Y ) of Banach function spaces is characterized, where X and Y satisfy uniformly a lower ℓ -estimate and uniformly an upper ℓ -estimate, respectively. The integral operator from X into Y of the form K f ( x ) = ϕ ( x ) ∫ 0 x k ( x , y ) f ( y ) ψ ( y ) d y is studied, where k , ϕ , ψ are prescribed functions under some local integrability conditions, the kernel k is non-negative and is assumed to satisfy certain...