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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 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.

Brushlet characterization of the Hardy space H1(R) and the space BMO.

Lasse Borup (2005)

Collectanea Mathematica

A typical wavelet system constitutes an unconditional basis for various function spaces -Lebesgue, Besov, Triebel-Lizorkin, Hardy, BMO. One of the main reasons is the frequency localization of an element from such a basis. In this paper we study a wavelet-type system, called a brushlet system. In [3] it was noticed that brushlets constitute unconditional bases for classical function spaces such as the Triebel-Lizorkin and Besov spaces. In this paper we study brushlet expansions of functions in the...

C 1 -smoothness of Nemytskii operators on Sobolev-type spaces of periodic functions

Irina Kmit (2011)

Commentationes Mathematicae Universitatis Carolinae

We consider a class of Nemytskii superposition operators that covers the nonlinear part of traveling wave models from laser dynamics, population dynamics, and chemical kinetics. Our main result is the C 1 -continuity property of these operators over Sobolev-type spaces of periodic functions.

C ( X ) can sometimes determine X without X being realcompact

Melvin Henriksen, Biswajit Mitra (2005)

Commentationes Mathematicae Universitatis Carolinae

As usual C ( X ) will denote the ring of real-valued continuous functions on a Tychonoff space X . It is well-known that if X and Y are realcompact spaces such that C ( X ) and C ( Y ) are isomorphic, then X and Y are homeomorphic; that is C ( X ) determines X . The restriction to realcompact spaces stems from the fact that C ( X ) and C ( υ X ) are isomorphic, where υ X is the (Hewitt) realcompactification of X . In this note, a class of locally compact spaces X that includes properly the class of locally compact realcompact spaces is exhibited...

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