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Displaying 41 – 60 of 85

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Boundedness from H 1 to L 1 of Riesz transforms on a Lie group of exponential growth

Peter Sjögren, Maria Vallarino (2008)

Annales de l’institut Fourier

Let G be the Lie group 2 + endowed with the Riemannian symmetric space structure. Let X 0 , X 1 , X 2 be a distinguished basis of left-invariant vector fields of the Lie algebra of G and define the Laplacian Δ = - ( X 0 2 + X 1 2 + X 2 2 ) . In this paper we consider the first order Riesz transforms R i = X i Δ - 1 / 2 and S i = Δ - 1 / 2 X i , for i = 0 , 1 , 2 . We prove that the operators R i , but not the S i , are bounded from the Hardy space H 1 to L 1 . We also show that the second-order Riesz transforms T i j = X i Δ - 1 X j are bounded from H 1 to L 1 , while the transforms S i j = Δ - 1 X i X j and R i j = X i X j Δ - 1 , for i , j = 0 , 1 , 2 , are not.

Boundedness of certain oscillatory singular integrals

Dashan Fan, Yibiao Pan (1995)

Studia Mathematica

We prove the L p and H 1 boundedness of oscillatory singular integral operators defined by Tf = p.v.Ω∗f, where Ω ( x ) = e i Φ ( x ) K ( x ) , K(x) is a Calderón-Zygmund kernel, and Φ satisfies certain growth conditions.

Boundedness of commutators of singular and potential operators in generalized grand Morrey spaces and some applications

Vakhtang Kokilashvili, Alexander Meskhi, Humberto Rafeiro (2013)

Studia Mathematica

In the setting of spaces of homogeneous type, it is shown that the commutator of Calderón-Zygmund type operators as well as the commutator of a potential operator with a BMO function are bounded in a generalized grand Morrey space. Interior estimates for solutions of elliptic equations are also given in the framework of generalized grand Morrey spaces.

Boundedness of commutators of strongly singular convolution operators on Herz-type spaces

Zongguang Liu (2003)

Studia Mathematica

The author investigates the boundedness of the higher order commutator of strongly singular convolution operator, T b m , on Herz spaces K ̇ q α , p ( ) and K q α , p ( ) , and on a new class of Herz-type Hardy spaces H K ̇ q , b , m α , p , 0 ( ) and H K q , b , m α , p , 0 ( ) , where 0 < p ≤ 1 < q < ∞, α = n(1-1/q) and b ∈ BMO(ℝⁿ).

Boundedness of Fourier integral operators on Fourier Lebesgue spaces and affine fibrations

Fabio Nicola (2010)

Studia Mathematica

We study Fourier integral operators of Hörmander’s type acting on the spaces L p ( d ) c o m p , 1 ≤ p ≤ ∞, of compactly supported distributions whose Fourier transform is in L p . We show that the sharp loss of derivatives for such an operator to be bounded on these spaces is related to the rank r of the Hessian of the phase Φ(x,η) with respect to the space variables x. Indeed, we show that operators of order m = -r|1/2-1/p| are bounded on L p ( d ) c o m p if the mapping x x Φ ( x , η ) is constant on the fibres, of codimension r, of an affine...

Boundedness of Hardy-Littlewood maximal operator in the framework of Lizorkin-Triebel spaces.

Soulaymane Korry (2002)

Revista Matemática Complutense

We describe a class O of nonlinear operators which are bounded on the Lizorkin-Triebel spaces Fsp,q(Rn), for 0 &lt; s &lt; 1 and 1 &lt; p, q &lt; ∞. As a corollary, we prove that the Hardy-Littlewood maximal operator is bounded on Fsp,q(Rn), for 0 &lt; s &lt; 1 and 1 &lt; p, q &lt; ∞ ; this extends the result of Kinnunen (1997), valid for the Sobolev space H1p(Rn).

Boundedness of Hardy-Littlewood maximal operator on block spaces with variable exponent

Ka Luen Cheung, Kwok-Pun Ho (2014)

Czechoslovak Mathematical Journal

The family of block spaces with variable exponents is introduced. We obtain some fundamental properties of the family of block spaces with variable exponents. They are Banach lattices and they are generalizations of the Lebesgue spaces with variable exponents. Moreover, the block space with variable exponents is a pre-dual of the corresponding Morrey space with variable exponents. The main result of this paper is on the boundedness of the Hardy-Littlewood maximal operator on the block space with...

Currently displaying 41 – 60 of 85