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Besov spaces on spaces of homogeneous type and fractals

Dachun Yang (2003)

Studia Mathematica

Let Γ be a compact d-set in ℝⁿ with 0 < d ≤ n, which includes various kinds of fractals. The author shows that the Besov spaces B p q s ( Γ ) defined by two different and equivalent methods, namely, via traces and quarkonial decompositions in the sense of Triebel are the same spaces as those obtained by regarding Γ as a space of homogeneous type when 0 < s < 1, 1 < p < ∞ and 1 ≤ q ≤ ∞.

Bilinear multipliers on Lorentz spaces

Francisco Villarroya (2008)

Czechoslovak Mathematical Journal

We give one sufficient and two necessary conditions for boundedness between Lebesgue or Lorentz spaces of several classes of bilinear multiplier operators closely connected with the bilinear Hilbert transform.

Bilinear operators associated with Schrödinger operators

Chin-Cheng Lin, Ying-Chieh Lin, Heping Liu, Yu Liu (2011)

Studia Mathematica

Let L = -Δ + V be a Schrödinger operator in d and H ¹ L ( d ) be the Hardy type space associated to L. We investigate the bilinear operators T⁺ and T¯ defined by T ± ( f , g ) ( x ) = ( T f ) ( x ) ( T g ) ( x ) ± ( T f ) ( x ) ( T g ) ( x ) , where T₁ and T₂ are Calderón-Zygmund operators related to L. Under some general conditions, we prove that either T⁺ or T¯ is bounded from L p ( d ) × L q ( d ) to H ¹ L ( d ) for 1 < p,q < ∞ with 1/p + 1/q = 1. Several examples satisfying these conditions are given. We also give a counterexample for which the classical Hardy space estimate fails.

Boundedness and compactness of some operators on discrete Morrey spaces

Martha Guzmán-Partida (2021)

Commentationes Mathematicae Universitatis Carolinae

We consider discrete versions of Morrey spaces introduced by Gunawan et al. in papers published in 2018 and 2019. We prove continuity and compactness of multiplication operators and commutators acting on them.

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 one-sided fractional integrals in the one-sided Calderón-Hardy spaces

Alejandra Perini (2011)

Commentationes Mathematicae Universitatis Carolinae

In this paper we study the mapping properties of the one-sided fractional integrals in the Calderón-Hardy spaces q , α p , + ( ω ) for 0 < p 1 , 0 < α < and 1 < q < . Specifically, we show that, for suitable values of p , q , γ , α and s , if ω A s + (Sawyer’s classes of weights) then the one-sided fractional integral I γ + can be extended to a bounded operator from q , α p , + ( ω ) to q , α + γ p , + ( ω ) . The result is a consequence of the pointwise inequality N q , α + γ + I γ + F ; x C α , γ N q , α + F ; x , where N q , α + ( F ; x ) denotes the Calderón maximal function.

Boundedness of some sublinear operators and commutators on Morrey-Herz spaces with variable exponents

Yan Lu, Yue Ping Zhu (2014)

Czechoslovak Mathematical Journal

We introduce a new type of variable exponent function spaces M K ˙ q , p ( · ) α ( · ) , λ ( n ) of Morrey-Herz type where the two main indices are variable exponents, and give some propositions of the introduced spaces. Under the assumption that the exponents α and p are subject to the log-decay continuity both at the origin and at infinity, we prove the boundedness of a wide class of sublinear operators satisfying a proper size condition which include maximal, potential and Calderón-Zygmund operators and their commutators of BMO...

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 p , q s ( ) to a quasi-Banach space ℬ if and only if sup | | T ( a ) | | : a is an infinitely differentiable (p,q,s)-atom of p , q s ( ) < ∞, where the (p,q,s)-atom of p , q s ( ) is as defined by Han, Paluszyński and Weiss.

Carleson measures for weighted harmonic mixed norm spaces on bounded domains in n

Ivana Savković (2022)

Czechoslovak Mathematical Journal

We study weighted mixed norm spaces of harmonic functions defined on smoothly bounded domains in n . Our principal result is a characterization of Carleson measures for these spaces. First, we obtain an equivalence of norms on these spaces. Then we give a necessary and sufficient condition for the embedding of the weighted harmonic mixed norm space into the corresponding mixed norm space.

CLO spaces and central maximal operators

Martha Guzmán-Partida (2013)

Archivum Mathematicum

We consider central versions of the space BLO studied by Coifman and Rochberg and later by Bennett, as well as some natural relations with a central version of a maximal operator.

Coefficient multipliers on spaces of vector-valued entire Dirichlet series

Sharma Akanksha, Girja S. Srivastava (2017)

Mathematica Bohemica

The spaces of entire functions represented by Dirichlet series have been studied by Hussein and Kamthan and others. In the present paper we consider the space X of all entire functions defined by vector-valued Dirichlet series and study the properties of a sequence space which is defined using the type of an entire function represented by vector-valued Dirichlet series. The main result concerns with obtaining the nature of the dual space of this sequence space and coefficient multipliers for some...

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