• 대한수학회지
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• 제35권2호
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• pp.361-370
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• 1998

A condition for a certain maximal operator to be of weak type (p, p) is studied. This operator unifies various maximal operators cited in the literatures.

• 대한수학회보
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• 제36권1호
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• pp.25-31
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• 1999

Let $\nu$ be a positive Borel measure on a space of homogeneous type (X, d, $\mu$), satisfying the doubling property. A condition on a weight $\omega$ for whixh a maximal operator $M\nu f$(x) defined by M$mu$f(x)=supr>0{{{{ { 1} over {ν(B(x,r)) } INT _{ B(x,r)} │f(y)│d mu (y)}}}}, is of weak type (p,p) with respect to (ν, $omega$), is that there exists a constant C such that C $omega$(y) for a.e. y$\in$B(x, r) if p=1, and {{{{( { 1} over { upsilon (B(x,r) } INT _{ B(x,r)}omega(y) ^ (-1/p-1) d mu (y))^(p-1)}}}} C, if 1$infty$.

• Korean Journal of Mathematics
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• 제28권3호
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• pp.489-507
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• 2020

In this paper we discussed some growth properties of entire functions of several complex variables on the basis of (p, q)-𝜑 relative Gol'dberg type and (p, q)-𝜑 relative Gol'dberg weal type where p, q are positive integers and 𝜑(R) : [0, +∞) → (0, +∞) is a non-decreasing unbounded function.

• Korean Journal of Mathematics
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• 제26권2호
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• pp.215-269
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• 2018

Orders and types of entire functions have been actively investigated by many authors. In this paper, we investigate some basic properties in connection with sum and product of relative (p, q, t) L-th order, relative (p, q, t) L-th type, and relative (p, q, t) L-th weak type of entire functions with respect to another entire function where $p,q{\in}{\mathbb{N}}$ and $t{\in}{\mathbb{N}}{\cup}\{-1,0\}$.

• East Asian mathematical journal
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• 제23권1호
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• pp.37-43
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• 2007

We study a maximal operator defined on spaces of homogeneous type, and we prove that this operator is of weak type (1,1). As a consequence we show that the maximal operator belongs to the Muckenhoupt's class $A_1$.

• Korean Journal of Mathematics
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• 제26권4호
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• pp.629-663
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• 2018

Let us suppose that ${\mathbb{K}}$ be a complete ultrametric algebraically closed field and $\mathcal{A}$ (${\mathbb{K}}$) be the ${\mathbb{K}}$-algebra of entire functions on K. The main aim of this paper is to study some newly developed results related to the growth rates of iterated p-adic entire functions on the basis of their relative orders, relative type and relative weak type.

• 호남수학학술지
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• 제41권3호
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• pp.463-487
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• 2019

In the paper we establish some new results depending on the comparative growth properties of composite entire and meromorphic functions using relative (p, q, t)L-th order and relative (p, q, t)L-th type of entire and meromorphic function with respect to another entire function.

• 대한수학회보
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• 제43권3호
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• pp.543-549
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• 2006

Sung et al. [13] obtained a WLLN (weak law of large numbers) for the array $\{X_{{ni},\;u_n{\leq}i{\leq}v_n,\;n{\leq}1\}$ of random variables under a Cesaro type condition, where $\{u_n{\geq}-{\infty},\;n{\geq}1\}$ and $\{v_n{\leq}+{\infty},\;n{\geq}1\}$ large two sequences of integers. In this paper, we extend the result of Sung et al. [13] to a martingale type p Banach space.

• 천문학회지
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• 제47권1호
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• pp.1-13
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• 2014

We analyze the dependence of disk morphology (arm class, Hubble type, bar type) of nearby spiral galaxies on the galaxy environment by using local background density (${\Sigma}_n$), projected distance ($r_p$), and tidal index (T I) as measures of the environment. There is a strong dependence of arm class and Hubble type on the galaxy environment, while the bar type exhibits a weak dependence with a high frequency of SB galaxies in high density regions. Grand design fractions and early-type fractions increase with increasing ${\Sigma}_n$, $1/r_p$, and T I, while fractions of flocculent spirals and late-type spirals decrease. Multiple-arm and intermediate-type spirals exhibit nearly constant fractions with weak trends similar to grand design and early-type spirals. While bar types show only a marginal dependence on ${\Sigma}_n$, they show a fairly clear dependence on $r_p$ with a high frequency of SB galaxies at small $r_p$. The arm class also exhibits a stronger correlation with $r_p$ than ${\Sigma}_n$ and T I, whereas the Hubble type exhibits similar correlations with ${\Sigma}_n$ and $r_p$. This suggests that the arm class is mostly affected by the nearest neighbor while the Hubble type is affected by the local densities contributed by neighboring galaxies as well as the nearest neighbor.

• Korean Journal of Mathematics
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• 제9권2호
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• pp.83-98
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• 2001

We characterize ($r,w$)-nuclear operators acting from a Banach space whose dual has weak type $q$ into a Banach space of weak type $p$ by the asymptotic behaviour of their entropy numbers.