Displaying 561 – 580 of 689

Showing per page

Trace inequalities for fractional integrals in grand Lebesgue spaces

Vakhtang Kokilashvili, Alexander Meskhi (2012)

Studia Mathematica

rning the boundedness for fractional maximal and potential operators defined on quasi-metric measure spaces from L p ) , θ ( X , μ ) to L q ) , q θ / p ( X , ν ) (trace inequality), where 1 < p < q < ∞, θ > 0 and μ satisfies the doubling condition in X. The results are new even for Euclidean spaces. For example, from our general results D. Adams-type necessary and sufficient conditions guaranteeing the trace inequality for fractional maximal functions and potentials defined on so-called s-sets in ℝⁿ follow. Trace inequalities...

Transference and restriction of maximal multiplier operators on Hardy spaces

Zhixin Liu, Shanzhen Lu (1993)

Studia Mathematica

The aim of this paper is to establish transference and restriction theorems for maximal operators defined by multipliers on the Hardy spaces H p ( n ) and H p ( n ) , 0 < p ≤ 1, which generalize the results of Kenig-Tomas for the case p > 1. We prove that under a mild regulation condition, an L ( n ) function m is a maximal multiplier on H p ( n ) if and only if it is a maximal multiplier on H p ( n ) . As an application, the restriction of maximal multipliers to lower dimensional Hardy spaces is considered.

Transference of weak type bounds of multiparameter ergodic and geometric maximal operators

Paul Hagelstein, Alexander Stokolos (2012)

Fundamenta Mathematicae

Let U , . . . , U d be a non-periodic collection of commuting measure preserving transformations on a probability space (Ω,Σ,μ). Also let Γ be a nonempty subset of d and the associated collection of rectangular parallelepipeds in d with sides parallel to the axes and dimensions of the form n × × n d with ( n , . . . , n d ) Γ . The associated multiparameter geometric and ergodic maximal operators M and M Γ are defined respectively on L ¹ ( d ) and L¹(Ω) by M g ( x ) = s u p x R 1 / | R | R | g ( y ) | d y and M Γ f ( ω ) = s u p ( n , . . . , n d ) Γ 1 / n n d j = 0 n - 1 j d = 0 n d - 1 | f ( U j U d j d ω ) | . Given a Young function Φ, it is shown that M satisfies the weak type estimate | x d : M g ( x ) > α | C d Φ ( c | g | / α ) for...

Translation averages of dyadic weights are not always good weights.

Lesley A. Ward (2002)

Revista Matemática Iberoamericana

The process of translation averaging is known to improve dyadic BMO to the space BMO of functions of bounded mean oscillation, in the sense that the translation average of a family of dyadic BMO functions is necessarily a BMO function. The present work investigates the effect of translation averaging in other dyadic settings. We show that translation averages of dyadic doubling measures need not be doubling measures, translation averages of dyadic Muckenhoupt weights need not be Muckenhoupt weights,...

Transmission of convergence

Neugebauer, Christoph J. (2003)

Nonlinear Analysis, Function Spaces and Applications

If E ( f ) = { x : lim sup f μ j ( x ) > lim inf f μ j ( x ) } , we examine the type of convergence of g k to f so that | E ( g k ) | M , k = 1 , 2 , , implies | E ( f ) | M .

Triebel-Lizorkin spaces for Hermite expansions

Jay Epperson (1995)

Studia Mathematica

This paper develops some Littlewood-Paley theory for Hermite expansions. The main result is that certain analogues of Triebel-Lizorkin spaces are well-defined in the context of Hermite expansions.

Triebel-Lizorkin spaces on spaces of homogeneous type

Y.-S. Han (1994)

Studia Mathematica

In [HS] the Besov and Triebel-Lizorkin spaces on spaces of homogeneous type were introduced. In this paper, the Triebel-Lizorkin spaces on spaces of homogeneous type are generalized to the case where p 0 < p 1 q < , and a new atomic decomposition for these spaces is obtained. As a consequence, we give the Littlewood-Paley characterization of Hardy spaces on spaces of homogeneous type which were introduced by the maximal function characterization in [MS2].

Triebel-Lizorkin spaces with non-doubling measures

Yongsheng Han, Dachun Yang (2004)

Studia Mathematica

Suppose that μ is a Radon measure on d , which may be non-doubling. The only condition assumed on μ is a growth condition, namely, there is a constant C₀ > 0 such that for all x ∈ supp(μ) and r > 0, μ(B(x,r)) ≤ C₀rⁿ, where 0 < n ≤ d. The authors provide a theory of Triebel-Lizorkin spaces p q s ( μ ) for 1 < p < ∞, 1 ≤ q ≤ ∞ and |s| < θ, where θ > 0 is a real number which depends on the non-doubling measure μ, C₀, n and d. The method does not use the vector-valued maximal function inequality...

Two problems on doubling measures.

Robert Kaufman, Jang-Mei Wu (1995)

Revista Matemática Iberoamericana

Doubling measures appear in relation to quasiconformal mappings of the unit disk of the complex plane onto itself. Each such map determines a homeomorphism of the unit circle on itself, and the problem arises, which mappings f can occur as boundary mappings?

Two results on the Dunkl maximal operator

Luc Deleaval (2011)

Studia Mathematica

In this article, we first improve the scalar maximal theorem for the Dunkl maximal operator by giving some precisions on the behavior of the constants of this theorem for a general reflection group. Next we complete the vector-valued theorem for the Dunkl-type Fefferman-Stein operator in the d case by establishing a result of exponential integrability corresponding to the case p = +∞.

Two weight norm inequalities for fractional one-sided maximal and integral operators

Liliana De Rosa (2006)

Commentationes Mathematicae Universitatis Carolinae

In this paper, we give a generalization of Fefferman-Stein inequality for the fractional one-sided maximal operator: - + M α + ( f ) ( x ) p w ( x ) d x A p - + | f ( x ) | p M α p - ( w ) ( x ) d x , where 0 < α < 1 and 1 < p < 1 / α . We also obtain a substitute of dual theorem and weighted norm inequalities for the one-sided fractional integral I α + .

Two weight norm inequality for the fractional maximal operator and the fractional integral operator.

Yves Rakotondratsimba (1998)

Publicacions Matemàtiques

New sufficient conditions on the weight functions u(.) and v(.) are given in order that the fractional maximal [resp. integral] operator Ms [resp. Is], 0 ≤ s &lt; n, [resp. 0 &lt; s &lt; n] sends the weighted Lebesgue space Lp(v(x)dx) into Lp(u(x)dx), 1 &lt; p &lt; ∞. As a consequence a characterization for this estimate is obtained whenever the weight functions are radial monotone.

Two weighted inequalities for convolution maximal operators.

Ana Lucía Bernardis, Francisco Javier Martín-Reyes (2002)

Publicacions Matemàtiques

Let φ: R → [0,∞) an integrable function such that φχ(-∞,0) = 0 and φ is decreasing in (0,∞). Let τhf(x) = f(x-h), with h ∈ R {0} and fR(x) = 1/R f(x/R), with R &gt; 0. In this paper we characterize the pair of weights (u, v) such that the operators Mτhφf(x) = supR&gt;0|f| * [τhφ]R(x) are of weak type (p, p) with respect to (u, v), 1 &lt; p &lt; ∞.

Two-parameter Hardy-Littlewood inequality and its variants

Chang-Pao Chen, Dah-Chin Luor (2000)

Studia Mathematica

Let s* denote the maximal function associated with the rectangular partial sums s m n ( x , y ) of a given double function series with coefficients c j k . The following generalized Hardy-Littlewood inequality is investigated: | | s * | | p , μ C p , α , β Σ j = 0 Σ k = 0 ( j ̅ ) p - α - 2 ( k ̅ ) p - β - 2 | c j k | p 1 / p , where ξ̅=max(ξ,1), 0 < p < ∞, and μ is a suitable positive Borel measure. We give sufficient conditions on c j k and μ under which the above Hardy-Littlewood inequality holds. Several variants of this inequality are also examined. As a consequence, the ||·||p,μ-convergence property of s m n ( x , y ) ...

Currently displaying 561 – 580 of 689