scholarly journals Lp‐Estimates for the ∂¯b‐equation on a class of infinite type domains

2020 ◽  
Author(s):  
Tran Vu Khanh ◽  
Andrew Raich
Keyword(s):  
Lp Estimates ◽  
Infinite Type

Lp estimates for the $\bar\partial$-equation on a class of infinite type domains

2014 ◽  
Vol 25 (11) ◽  
pp. 1450106 ◽  
Author(s):  
Ly Kim Ha ◽  
Tran Vu Khanh ◽  
Andrew Raich
Keyword(s):  
Lp Estimates ◽  
Infinite Type ◽  
Cauchy Riemann

We prove Lp estimates, 1 ≤ p ≤ ∞, for solutions to the Cauchy–Riemann equations [Formula: see text] on a class of infinite type domains in ℂ2. The domains under consideration are a class of convex ellipsoids, and we show that if ϕ is a [Formula: see text]-closed (0, 1)-form with coefficients in Lp and u is the Henkin kernel solution to [Formula: see text], then ‖u‖p ≤ C‖ϕ‖p where the constant C is independent of ϕ. In particular, we prove L1 estimates and obtain Lp estimates by interpolation.

scholarly journals Random additions in urns of integers

2021 ◽  
Vol 58 (2) ◽  
pp. 335-346
Author(s):  
Mackenzie Simper
Keyword(s):  
Finite Group ◽  
Random Process ◽  
Uniform Distribution ◽  
Discrete Time ◽  
Random Variable ◽  
Urn Model ◽  
Infinite Type ◽  
The Mean ◽  
A Finite Group ◽  
Proof Of Convergence

AbstractConsider an urn containing balls labeled with integer values. Define a discrete-time random process by drawing two balls, one at a time and with replacement, and noting the labels. Add a new ball labeled with the sum of the two drawn labels. This model was introduced by Siegmund and Yakir (2005) Ann. Prob.33, 2036 for labels taking values in a finite group, in which case the distribution defined by the urn converges to the uniform distribution on the group. For the urn of integers, the main result of this paper is an exponential limit law. The mean of the exponential is a random variable with distribution depending on the starting configuration. This is a novel urn model which combines multi-drawing and an infinite type of balls. The proof of convergence uses the contraction method for recursive distributional equations.

scholarly journals On some Lp-estimates for hyperbolic equations

1992 ◽  
Vol 30 (1-2) ◽  
pp. 149-163 ◽  
Author(s):  
Mitsuru Sugimoto
Keyword(s):  
Hyperbolic Equations ◽  
Lp Estimates

scholarly journals Alvis–Curtis duality for representations of reductive groups with Frobenius maps

2020 ◽  
Vol 32 (5) ◽  
pp. 1289-1296
Author(s):  
Junbin Dong
Keyword(s):  
Irreducible Representations ◽  
Reductive Groups ◽  
Infinite Type ◽  
Abstract Representations

AbstractWe generalize the Alvis–Curtis duality to the abstract representations of reductive groups with Frobenius maps. Similar to the case of representations of finite reductive groups, we show that the Alvis–Curtis duality of infinite type, which we define in this paper, also interchanges the irreducible representations in the principal representation category.

On a conjecture in Artin groups

2021 ◽  
pp. 1-25
Author(s):  
Arye Juhász
Keyword(s):  
Artin Group ◽  
Two Dimensional ◽  
Artin Groups ◽  
Small Cancellation ◽  
Small Cancellation Theory ◽  
Infinite Type ◽  
Trivial Center

It is conjectured that an irreducible Artin group which is of infinite type has trivial center. The conjecture is known to be true for two-dimensional Artin groups and for a few other types of Artin groups. In this work, we show that the conjecture holds true for Artin groups which satisfy a condition stronger than being of infinite type. We use small cancellation theory of relative presentations.

Upper lp-estimates in vector sequence spaces, with some applications

1993 ◽  
Vol 113 (2) ◽  
pp. 329-334 ◽  
Author(s):  
Jesús M. F. Castillo ◽  
Fernando Sánchez
Keyword(s):  
Banach Spaces ◽  
Sequence Space ◽  
Sequence Spaces ◽  
Vector Sequence ◽  
Lp Estimates ◽  
Banach Sequence Space ◽  
Banach Sequence

In [11], Partington proved that if λ is a Banach sequence space with a monotone basis having the Banach-Saks property, and (Xn) is a sequence of Banach spaces each having the Banach-Saks property, then the vector sequence space ΣλXn has this same property. In addition, Partington gave an example showing that if λ and each Xn, have the weak Banach-Saks property, then ΣλXn need not have the weak Banach-Saks property.

scholarly journals A dual approach to Burkholder's Lp estimates

2021 ◽  
Author(s):  
Rodrigo Bañuelos ◽  
Tomasz Gałązka ◽  
Adam Osękowski
Keyword(s):  
Dual Approach ◽  
Lp Estimates

Circle homeomorphism with infinite type of singularities

2015 ◽  
Author(s):  
Sokhobiddin Akhatkulov ◽  
Mohd. Salmi Md. Noorani
Keyword(s):  
Circle Homeomorphism ◽  
Infinite Type
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