Displaying similar documents to “Littlewood-Paley decompositions and Fourier multipliers with singularities on certain sets”

Semivariation in L p -spaces

Brian Jefferies, Susumu Okada (2005)

Commentationes Mathematicae Universitatis Carolinae

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Suppose that X and Y are Banach spaces and that the Banach space X ⊗ ^ τ Y is their complete tensor product with respect to some tensor product topology τ . A uniformly bounded X -valued function need not be integrable in X ⊗ ^ τ Y with respect to a Y -valued measure, unless, say, X and Y are Hilbert spaces and τ is the Hilbert space tensor product topology, in which case Grothendieck’s theorem may be applied. In this paper, we take an index 1 ≤ p < ∞ and suppose that X and Y are L p -spaces with τ p the associated...

Cesàro summability of one- and two-dimensional trigonometric-Fourier series

Ferenc Weisz (1997)

Colloquium Mathematicae

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We introduce p-quasilocal operators and prove that if a sublinear operator T is p-quasilocal and bounded from L ∞ to L ∞ then it is also bounded from the classical Hardy space H p ( T ) to L p (0 < p ≤ 1). As an application it is shown that the maximal operator of the one-parameter Cesàro means of a distribution is bounded from H p ( T ) to L p (3/4 < p ≤ ∞) and is of weak type ( L 1 , L 1 ) . We define the two-dimensional dyadic hybrid Hardy space H 1 ♯ ( T 2 ) and verify that the maximal operator of the Cesàro means of a two-dimensional...

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...