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Boundedness of generalized fractional integral operators on Orlicz spaces near L 1 over metric measure spaces

Daiki Hashimoto, Takao Ohno, Tetsu Shimomura (2019)

Czechoslovak Mathematical Journal

We are concerned with the boundedness of generalized fractional integral operators I ρ , τ from Orlicz spaces L Φ ( X ) near L 1 ( X ) to Orlicz spaces L Ψ ( X ) over metric measure spaces equipped with lower Ahlfors Q -regular measures, where Φ is a function of the form Φ ( r ) = r ℓ ( r ) and ℓ is of log-type. We give a generalization of paper by Mizuta et al. (2010), in the Euclidean setting. We deal with both generalized Riesz potentials and generalized logarithmic potentials.

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 < s < 1 and 1 < p, q < ∞. As a corollary, we prove that the Hardy-Littlewood maximal operator is bounded on Fsp,q(Rn), for 0 < s < 1 and 1 < p, q < ∞ ; 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...

Boundedness of linear maps

T. S. S. R. K. Rao (2000)

Commentationes Mathematicae Universitatis Carolinae

In this short note we consider necessary and sufficient conditions on normed linear spaces, that ensure the boundedness of any linear map whose adjoint maps extreme points of the unit ball of the domain space to continuous linear functionals.

Boundedness of Littlewood-Paley operators relative to non-isotropic dilations

Shuichi Sato (2019)

Czechoslovak Mathematical Journal

We consider Littlewood-Paley functions associated with a non-isotropic dilation group on ℝ n . We prove that certain Littlewood-Paley functions defined by kernels with no regularity concerning smoothness are bounded on weighted L p spaces, 1 < p < ∞ , with weights of the Muckenhoupt class. This, in particular, generalizes a result of N. Rivière (1971).

Boundedness of sublinear operators in Triebel-Lizorkin spaces via atoms

Liguang Liu, Dachun Yang (2009)

Studia Mathematica

Let s ∈ ℝ, p ∈ (0,1] and q ∈ [p,∞). It is proved that a sublinear operator T uniquely extends to a bounded sublinear operator from the Triebel-Lizorkin space Ḟ p , q s ( ℝ ⁿ ) to a quasi-Banach space ℬ if and only if sup | | T ( a ) | | ℬ : a is an infinitely differentiable (p,q,s)-atom of Ḟ p , q s ( ℝ ⁿ ) < ∞, where the (p,q,s)-atom of Ḟ p , q s ( ℝ ⁿ ) is as defined by Han, Paluszyński and Weiss.

Bounds for the spectral radius of positive operators

Roman Drnovšek (2000)

Commentationes Mathematicae Universitatis Carolinae

Let f be a non-zero positive vector of a Banach lattice L , and let T be a positive linear operator on L with the spectral radius r ( T ) . We find some groups of assumptions on L , T and f under which the inequalities sup { c ≥ 0 : T f ≥ c f } ≤ r ( T ) ≤ inf { c ≥ 0 : T f ≤ c f } hold. An application of our results gives simple upper and lower bounds for the spectral radius of a product of positive operators in terms of positive eigenvectors corresponding to the spectral radii of given operators. We thus extend the matrix result obtained by Johnson and Bru which...

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