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Lacunary sequence spaces defined by Musielak-Orlicz function
Le Matematiche, 2013 In this paper we introduce lacunary sequence spaces defined by a Musielak-Orlicz function M = (M_k) and a sequence of modulus functions F = (f_k). We also make an effort to study some topological properties and inclusion relations between these spaces.
Kuldip Raj, Sunil K. Sharma
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Taming the Natural Boundary of Centered Polygonal Lacunary Functions—Restriction to the Symmetry Angle Space [PDF]
Mathematics, 2020 This work investigates centered polygonal lacunary functions restricted from the unit disk onto symmetry angle space which is defined by the symmetry angles of a given centered polygonal lacunary function. This restriction allows for one to consider only
Leah K. Mork +2 more
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Exploration of Filled-In Julia Sets Arising from Centered Polygonal Lacunary Functions [PDF]
Fractal and Fractional, 2019 Centered polygonal lacunary functions are a particular type of lacunary function that exhibit properties which set them apart from other lacunary functions. Primarily, centered polygonal lacunary functions have true rotational symmetry.
L.K. Mork +4 more
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Lacunary partition functions [PDF]
Mathematical Research Letters, 2002 A function \(f(q)\) is lacunary if \(f(q)= \sum_{n\geq 0} a(n)q^n\) and \(a(n)\) is almost always \(0\). It is known by the work of J.-P. Serre, B. Gordon and S. Robins that there are approximately 60 pairs \((r,s)\) for which \[ \prod_{n=1}^\infty (1-q^n)^r(1-q^{2n})^s \] is lacunary.
Jeremy Lovejoy
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Rotationally Symmetric Lacunary Functions and Products of Centered Polygonal Lacunary Functions [PDF]
Fractal and Fractional, 2020 This work builds upon previous studies of centered polygonal lacunary functions by presenting proofs of theorems showing how rotational and dihedral mirror symmetry manifest in these lacunary functions at the modulus level.
L. K. Mork +3 more
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Lacunary maximal functions on homogeneous groups [PDF]
Journal of Functional Analysis, 2023 20 pages, 1 table, no ...
Aswin Govindan Sheri +2 more
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Bounds for lacunary bilinear spherical and triangle maximal functions [PDF]
Journal of Fourier Analysis and Applications, 2023 We prove $L^p\times L^q\rightarrow L^r$ bounds for certain lacunary bilinear maximal averaging operators with parameters satisfying the Hölder relation $1/p+1/q=1/r$. The boundedness region that we get contains at least the interior of the Hölder boundedness region of the associated single scale bilinear averaging operator.
Tainara Borges, Benjamin R. Foster
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More lacunary partition functions [PDF]
Illinois Journal of Mathematics, 2003 Let \(Q_{m,k}(n)\) denote the number of partitions of \(n\) into distinct parts \(\lambda_i\) such that (i) each \(\lambda_i\equiv 0\), \(m\pmod k\); (ii) the least part \(\lambda_1\equiv 0\pmod k\); (iii) \(2\lambda_1+ m\) does not occur as a part. Let \(Q_{m,k}^{\pm}(n)\) denote respectively the number of such partitions into evenly, oddly many parts.
Jeremy Lovejoy
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Problems on averages and lacunary maximal functions [PDF]
Banach Center Publications, 2011 We prove three results concerning convolution operators and lacunary maximal functions associated to dilates of measures. First, we obtain an $H^1$ to $L^{1,\infty}$ bound for lacunary maximal operators under a dimensional assumption on the underlying ...
Seeger, Andreas, Wright, James
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Weighted Lacunary Maximal Functions on Curves [PDF]
Canadian Mathematical Bulletin, 1995 AbstractLet γ(t) = (t, t2,..., tn) + a be a curve in Rn, where n ≥ 2 and a ∊ Rn. We prove LP-Lq estimates for the weighted lacunary maximal function, related to this curve, defined byIf n = 2 or 3 our results are (nearly) sharp.
Jong-Guk Bak
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