scholarly journals THE RATE OF INCREASE OF MEAN VALUES OF FUNCTIONS IN HARDY SPACES

2009 ◽  
Vol 86 (2) ◽  
pp. 199-204
Author(s):  
JAVAD MASHREGHI
Keyword(s):  
Hardy Space ◽  
Hardy Spaces ◽  
Mean Values ◽  
Rate Of Increase

AbstractThe norm of a function f in the Hardy space Hp(𝔻) is by definition the limit of $\|f_r\|_p$ as r→1. We show that $d \|f_r\|_p/dr$ grows at most like o(1/log r) as r→1.

New variable martingale Hardy spaces

2021 ◽  
pp. 1-29
Author(s):  
Yong Jiao ◽  
Dan Zeng ◽  
Dejian Zhou
Keyword(s):  
Brownian Motion ◽  
Hardy Space ◽  
Hardy Spaces ◽  
Stochastic Integral ◽  
Lebesgue Spaces ◽  
Type Space ◽  
Variable Lebesgue Spaces ◽  
Martingale Inequalities

We investigate various variable martingale Hardy spaces corresponding to variable Lebesgue spaces $\mathcal {L}_{p(\cdot )}$ defined by rearrangement functions. In particular, we show that the dual of martingale variable Hardy space $\mathcal {H}_{p(\cdot )}^{s}$ with $0<p_{-}\leq p_{+}\leq 1$ can be described as a BMO-type space and establish martingale inequalities among these martingale Hardy spaces. Furthermore, we give an application of martingale inequalities in stochastic integral with Brownian motion.

Non-tangential Maximal Function Characterizations of Hardy Spaces Associated with Degenerate Elliptic Operators

2015 ◽  
Vol 67 (5) ◽  
pp. 1161-1200 ◽  
Author(s):  
Junqiang Zhang ◽  
Jun Cao ◽  
Renjin Jiang ◽  
Dachun Yang
Keyword(s):  
Hardy Space ◽  
Maximal Function ◽  
Hardy Spaces ◽  
Riesz Transform ◽  
Degenerate Elliptic Operators ◽  
Degenerate Elliptic Operator ◽  
Muckenhoupt Class ◽  
Degenerate Elliptic ◽  
Function Characterization

AbstractLet w be either in the Muckenhoupt class of A2(ℝn) weights or in the class of QC(ℝn) weights, and let be the degenerate elliptic operator on the Euclidean space ℝn, n ≥ 2. In this article, the authors establish the non-tangential maximal function characterization of the Hardy space associated with , and when with , the authors prove that the associated Riesz transform is bounded from to the weighted classical Hardy space .

Modulus of continuity and convergence of subsequences of Vilenkin–Fejér means in martingale Hardy spaces

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Giorgi Tutberidze
Keyword(s):  
Hardy Space ◽  
Modulus Of Continuity ◽  
Hardy Spaces ◽  
Lebesgue Space ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Fejér Means ◽  
Necessary And Sufficient

Abstract In this paper, we find a necessary and sufficient condition for the modulus of continuity for which subsequences of Fejér means with respect to Vilenkin systems are bounded from the Hardy space H p {H_{p}} to the Lebesgue space L p {L_{p}} for all 0 < p < 1 2 {0<p<\frac{1}{2}} .

scholarly journals Factorizations of outer functions and extremal problems

1996 ◽  
Vol 39 (3) ◽  
pp. 535-546 ◽  
Author(s):  
Takahiko Nakazi
Keyword(s):  
Hardy Space ◽  
Hardy Spaces ◽  
Extremal Problems ◽  
The Other ◽  
Outer Function ◽  
Inner Functions ◽  
Special Case ◽  
Class Of Functions

The author has proved that an outer function in the Hardy space H1 can be factored into a product in which one factor is strongly outer and the other is the sum of two inner functions. In an endeavor to understand better the latter factor, we introduce a class of functions containing sums of inner functions as a special case. Using it, we describe the solutions of extremal problems in the Hardy spaces Hp for 1≦p<∞.

scholarly journals Marcinkiewicz Integrals on Weighted Weak Hardy Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Yue Hu ◽  
Yueshan Wang
Keyword(s):  
Hardy Space ◽  
Hardy Spaces ◽  
Lebesgue Space ◽  
Muckenhoupt Weight ◽  
Marcinkiewicz Integral ◽  
Smoothness Condition ◽  
Weight Class ◽  
Marcinkiewicz Integrals ◽  
Weak Hardy Space ◽  
Weak Lebesgue Space

We prove that, under the conditionΩ∈Lipα, Marcinkiewicz integralμΩis bounded from weighted weak Hardy spaceWHwpRnto weighted weak Lebesgue spaceWLwpRnformaxn/n+1/2,n/n+α<p≤1, wherewbelongs to the Muckenhoupt weight class. We also give weaker smoothness condition assumed on Ω to imply the boundedness ofμΩfromWHw1ℝntoWLw1Rn.

BOUNDEDNESS OF SEVERAL INTEGRAL OPERATORS WITH BOUNDED VARIABLE KERNELS ON HARDY AND WEAK HARDY SPACES

2013 ◽  
Vol 24 (12) ◽  
pp. 1350095 ◽  
Author(s):  
HUA WANG
Keyword(s):  
Hardy Space ◽  
Hardy Spaces ◽  
Atomic Decomposition ◽  
Integral Operators ◽  
Fractional Integrals ◽  
Variable Kernel ◽  
Marcinkiewicz Integrals ◽  
Decomposition Theory ◽  
Logarithmic Type ◽  
Lipschitz Conditions

In this paper, by using the atomic decomposition theory of Hardy space H1(ℝn) and weak Hardy space WH1(ℝn), we give the boundedness properties of some operators with variable kernels such as singular integral operators, fractional integrals and parametric Marcinkiewicz integrals on these spaces, under certain logarithmic type Lipschitz conditions assumed on the variable kernel Ω(x, z).

scholarly journals Notes on boundedness of spectral multipliers on Hardy spaces associated to operators

2011 ◽  
Vol 203 ◽  
pp. 109-122
Author(s):  
Bui The Anh
Keyword(s):  
Hardy Space ◽  
Hardy Spaces ◽  
Analytic Semigroup ◽  
Adjoint Operator ◽  
Upper Bounds ◽  
Space Of Homogeneous Type ◽  
Homogeneous Type ◽  
Spectral Multipliers ◽  
Spectral Multiplier ◽  
Suitable Function

AbstractLetLbe a nonnegative self-adjoint operator onL2(X), whereXis a space of homogeneous type. Assume thatLgenerates an analytic semigroupe–tlwhose kernel satisfies the standard Gaussian upper bounds. We prove that the spectral multiplierF(L) is bounded onfor 0&lt; p&lt; 1, the Hardy space associated to operatorL, whenFis a suitable function.

scholarly journals Hardy spaces estimates for multilinear operators with homogeneous kernels

2003 ◽  
Vol 170 ◽  
pp. 117-133 ◽  
Author(s):  
Yong Ding ◽  
Shanzhen Lu
Keyword(s):  
Hardy Space ◽  
Hardy Spaces ◽  
Fractional Integral ◽  
Integral Operators ◽  
Kernel Functions ◽  
Multilinear Operators ◽  
Product Spaces ◽  
Bounded Operators ◽  
Fractional Integral Operators ◽  
Bmo Function

AbstractIn this paper the authors prove that a class of multilinear operators formed by the singular integral or fractional integral operators with homogeneous kernels are bounded operators from the product spaces Lp1 × Lp2 × · · · × LpK (ℝn) to the Hardy spaces Hq (ℝn) and the weak Hardy space Hq,∞(ℝn), where the kernel functions Ωij satisfy only the Ls-Dini conditions. As an application of this result, we obtain the (Lp, Lq) boundedness for a class of commutator of the fractional integral with homogeneous kernels and BMO function.

scholarly journals The Rate of Increase of Mean Values of Functions in Weighted Hardy-Orlicz Spaces

2015 ◽  
Vol 61 (1) ◽  
pp. 161-168
Author(s):  
Ajay K. Sharma ◽  
Ambika Bhat
Keyword(s):  
Orlicz Space ◽  
Orlicz Spaces ◽  
Mean Values ◽  
Rate Of Increase

Abstract Let 0 ≤ q < ∞. For each f in the weighted Hardy-Orlicz space HΦ,q we show that grows at most like o(1/1 − r) as r → 1.

scholarly journals Fredholm Weighted Composition Operator on Weighted Hardy Space

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Liankuo Zhao
Keyword(s):  
Hardy Space ◽  
Composition Operator ◽  
Hardy Spaces ◽  
Weighted Composition Operator ◽  
Weighted Hardy Space ◽  
Weighted Hardy Spaces ◽  
Weighted Composition

This paper gives a unified characterization of Fredholm weighted composition operator on a class of weighted Hardy spaces.

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