Results 11 to 20 of about 3,983,040 (155)
Some inequalities related to strong convergence of Riesz logarithmic means
Journal of Inequalities and Applications, 2020 In this paper we derive a new strong convergence theorem of Riesz logarithmic means of the one-dimensional Vilenkin–Fourier (Walsh–Fourier) series. The corresponding inequality is pointed out and it is also proved that the inequality is in a sense sharp,
D. Lukkassen +3 more
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One‐Sided Version of Law of the Iterated Logarithm for Summations of Signum Functions
Journal of Mathematics, Volume 2023, Issue 1, 2023., 2023 The law of the iterated logarithm (LIL), which describes the rate of convergence for a convergent lacunary series, was established by R. Salem and A. Zygmund. This rate is determined based on the variance‐like term of the remainder after n terms of the series.
Santosh Ghimire, Kenan Yildirim
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Convergence of Vilenkin–Fourier series in variable Hardy spaces
Mathematische Nachrichten, Volume 295, Issue 9, Page 1812-1839, September 2022., 2022 Abstract Let p(·):[0,1)→(0,∞)$p(\cdot ): [0,1)\rightarrow (0,\infty )$ be a variable exponent function satisfying the log‐Hölder condition and 0
Ferenc Weisz
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Dyadic product BMO in the Bloom setting
Journal of the London Mathematical Society, Volume 106, Issue 2, Page 899-935, September 2022., 2022 Abstract Ó. Blasco and S. Pott showed that the supremum of operator norms over L2$L^2$ of all bicommutators (with the same symbol) of one‐parameter Haar multipliers dominates the biparameter dyadic product BMO norm of the symbol itself. In the present work we extend this result to the Bloom setting, and to any exponent 1
Spyridon Kakaroumpas +1 more
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Maximal regularity for the Cauchy problem of the heat equation in BMO
Mathematische Nachrichten, Volume 295, Issue 7, Page 1406-1442, July 2022., 2022 Abstract We consider maximal regularity for the Cauchy problem of the heat equation in a class of bounded mean oscillations (BMO$BMO$). Maximal regularity for non‐reflexive Banach spaces is not obtained by the established abstract theory. Based on the symmetric characterization of BMO$BMO$‐expression, we obtain maximal regularity for the heat equation ...
Takayoshi Ogawa, Senjo Shimizu
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Atomic decomposition of predictable martingale Hardy space with variable exponents [PDF]
, 2015 summary:This paper is mainly devoted to establishing an atomic decomposition of a predictable martingale Hardy space with variable exponents defined on probability spaces.
Hao, Zhiwei
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Journal of Function Spaces, Volume 2022, Issue 1, 2022., 2022 In this paper, we introduce the generalized grand Morrey spaces in the framework of probability space setting in the spirit of the martingale theory and grand Morrey spaces. The Doob maximal inequalities on the generalized grand Morrey spaces are provided.
Libo Li +3 more
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Bilateral Harnack Inequalities for Stochastic Differential Equation with Multiplicative Noise
Journal of Function Spaces, Volume 2022, Issue 1, 2022., 2022 By constructing a coupling with unbounded time‐dependent drift, a lower bound estimate of dimension‐free Harnack inequality with power is obtained for a large class of stochastic differential equation with multiplicative noise. The key is an application of the inverse Hölder inequality.
Zihao An +2 more
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A sufficient condition for the boundedness of operator-weighted martingale transforms and Hilbert transform [PDF]
, 2007 Let W be an operator weight taking values almost everywhere in the bounded positive invertible linear operators on a separable Hilbert space H. We show that if W and its inverse W−1 both satisfy a matrix reverse Holder property introduced in [2], then ...
Pott, S.
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Journal of Function Spaces, Volume 2022, Issue 1, 2022., 2022 Let θ ≥ 0 and p(·) be a variable exponent, and we introduce a new class of function spaces Lp(·),θ in a probabilistic setting which unifies and generalizes the variable Lebesgue spaces with θ = 0 and grand Lebesgue spaces with p(·) ≡ p and θ = 1. Based on the new spaces, we introduce a kind of Hardy‐type spaces, grand martingale Hardy spaces with ...
Libo Li, Zhiwei Hao, Tianqing An
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