scholarly journals Improved Hölder and reverse Hölder inequalities for Gaussian random vectors

2015 ◽  
Vol 280 ◽  
pp. 643-689 ◽  
Author(s):  
Wei-Kuo Chen ◽  
Nikos Dafnis ◽  
Grigoris Paouris
Keyword(s):  
Random Vectors ◽  
Reverse Hölder Inequalities ◽  
Reverse Hölder

scholarly journals Lp Estimates for Weak Solutions to Nonlinear Degenerate Parabolic Systems

2017 ◽  
Vol 2017 ◽  
pp. 1-12
Author(s):  
Na Wei ◽  
Xiangyu Ge ◽  
Yonghong Wu ◽  
Leina Zhao
Keyword(s):  
Weak Solutions ◽  
Vector Fields ◽  
Parabolic Systems ◽  
Growth Conditions ◽  
Lp Estimates ◽  
Reverse Hölder Inequalities ◽  
Degenerate Parabolic Systems ◽  
Degenerate Parabolic ◽  
Reverse Hölder ◽  
Nonlinear Degenerate

This paper is devoted to the Lp estimates for weak solutions to nonlinear degenerate parabolic systems related to Hörmander’s vector fields. The reverse Hölder inequalities for degenerate parabolic system under the controllable growth conditions and natural growth conditions are established, respectively, and an important multiplicative inequality is proved; finally, we obtain the Lp estimates for the weak solutions by combining the results of Gianazza and the Caccioppoli inequality.

scholarly journals Reverse Hölder Inequalities and Approximation Spaces

2001 ◽  
Vol 109 (1) ◽  
pp. 82-109 ◽  
Author(s):  
Joaquim Martı́n ◽  
Mario Milman
Keyword(s):  
Approximation Spaces ◽  
Reverse Hölder Inequalities ◽  
Reverse Hölder

scholarly journals Higher integrability for the singular porous medium system

2020 ◽  
Vol 2020 (767) ◽  
pp. 203-230 ◽  
Author(s):  
Verena Bögelein ◽  
Frank Duzaar ◽  
Christoph Scheven
Keyword(s):  
Porous Medium ◽  
Spatial Gradient ◽  
Fast Diffusion ◽  
The Novel ◽  
Higher Integrability ◽  
Reverse Hölder Inequalities ◽  
Diffusion Systems ◽  
Natural Range ◽  
Regularity Results ◽  
Reverse Hölder

AbstractIn this paper we establish in the fast diffusion range the higher integrability of the spatial gradient of weak solutions to porous medium systems. The result comes along with an explicit reverse Hölder inequality for the gradient. The novel feature in the proof is a suitable intrinsic scaling for space-time cylinders combined with reverse Hölder inequalities and a Vitali covering argument within this geometry. The main result holds for the natural range of parameters suggested by other regularity results. Our result applies to general fast diffusion systems and includes both, non-negative and signed solutions in the case of equations. The methods of proof are purely vectorial in their structure.

scholarly journals Higher integrability and reverse Hölder inequalities in the limit cases

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Arturo Popoli
Keyword(s):  
Hölder Inequality ◽  
Muckenhoupt Weights ◽  
Reverse Hölder Inequality ◽  
Higher Integrability ◽  
Reverse Hölder Inequalities ◽  
Reverse Hölder

Abstract We study the higher integrability of weights satisfying a reverse Hölder inequality ( ⨏ I u β ) 1 β ≤ B ⁢ ( ⨏ I u α ) 1 α {\biggl{(}\fint_{I}u^{\beta}\biggr{)}^{\frac{1}{\beta}}}\leq B{\biggl{(}\fint_{I}u^{\alpha}\biggr{)}^{\frac{1}{\alpha}}} for some B > 1 B>1 and given α < β \alpha<\beta , in the limit cases when α ∈ { - ∞ , 0 } \alpha\in\{-\infty,0\} and/or β ∈ { 0 , + ∞ } \beta\in\{0,+\infty\} . The results apply to the Gehring and Muckenhoupt weights and their corresponding limit classes.

Dyadic weights on $\mathbb {R}^n$ and reverse Hölder inequalities

2016 ◽  
pp. 1-10
Author(s):  
Eleftherios N. Nikolidakis ◽  
Antonios D. Melas
Keyword(s):  
Reverse Hölder Inequalities ◽  
Reverse Hölder

scholarly journals NEW GENERALIZATIONS IN THE SENSE OF THE WEIGHTED NON-SINGULAR FRACTIONAL INTEGRAL OPERATOR

Fractals ◽  
2020 ◽  
Vol 28 (08) ◽  
pp. 2040003 ◽  
Author(s):  
SAIMA RASHID ◽  
ZAKIA HAMMOUCH ◽  
DUMITRU BALEANU ◽  
YU-MING CHU
Keyword(s):  
Integral Operator ◽  
Weight Function ◽  
Fractional Integral ◽  
Fractional Integral Operator ◽  
Fractional Operator ◽  
Fractional Operators ◽  
Reverse Hölder Inequalities ◽  
Reverse Hölder

In this paper, we propose a new fractional operator which is based on the weight function for Atangana–Baleanu [Formula: see text]-fractional operators. A motivating characteristic is the generalization of classical variants within the weighted [Formula: see text]-fractional integral. We aim to establish Minkowski and reverse Hölder inequalities by employing weighted [Formula: see text]-fractional integral. The consequences demonstrate that the obtained technique is well-organized and appropriate.

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