• Journal of the Korean Mathematical Society
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• v.35 no.2
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• pp.295-314
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• 1998

In this article we examine certain distinctive features regarding Hardy spaces of both classical and product notions on $R^{N}$ with our focus on their interrelations through embeddings and restrictions. Applications of our results to multiple singular integrals are included.d.

• Honam Mathematical Journal
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• v.43 no.1
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• pp.26-34
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• 2021

In this paper two interesting double integrals involving product of two generalized hypergeometric functions have been evaluated in terms of gamma function. The results are derived with the help of known integrals involving hypergeometric functions recorded in the paper of Rathie et al. [6]. We also give several very interesting special cases.

• Kyungpook Mathematical Journal
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• v.46 no.3
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• pp.377-387
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• 2006

In this paper, we study the $L^p$ mapping properties of singular integral operators related to homogeneous mappings on product spaces with kernels which belong to $L(log^+\;L)^2$. Our results extend as well as improve some known results on singular integrals.

• Kyungpook Mathematical Journal
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• v.46 no.3
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• pp.307-313
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• 2006

In this paper, we first establish an interesting new finite integral whose integrand involves the product of a general class of polynomials introduced by Srivastava [13] and the generalized H-function ([9], [10]) having general argument. Next, we present five special cases of our main integral which are also quite general in nature and of interest by themselves. The first three integrals involve the product of $\bar{H}$-function with Jacobi polynomial, the product of two Jacobi polynomials and the product of two general binomial factors respectively. The fourth integral involves product of Jacobi polynomial and well known Fox's H-function and the last integral involves product of a Jacobi polynomial and 'g' function connected with a certain class of Feynman integral which may have practical applications.

• Honam Mathematical Journal
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• v.41 no.1
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• pp.1-17
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• 2019

The aim of this paper is to establish certain integrals involving product of the Aleph function with exponential function and multi Gauss's hypergeometric function. Being unified and general in nature, these integrals yield a number of known and new results as special cases. For the sake of illustration, twelve corollaries are also recorded here as special case of our main results.

• Journal of the Korean Mathematical Society
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• v.33 no.2
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• pp.319-332
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• 1996

Many authors have studied multiple stochastic integrals in pursuit of the existence of product processes in terms of multiple integrals. But there has not been much research into the structure of the product processes themselves. In this direction, a study which gives emphasis on sample path continuity and boundedness properties was initiated in Pyke[9]. For details of problem set-ups and necessary notations, see [9]. Recently the weak limits of U-processes are shown to be chaos processes, which is product of the same Brownian measures, see [2] and [7].

• Honam Mathematical Journal
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• v.35 no.4
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• pp.667-677
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• 2013

A remarkably large number of integrals involving a product of certain combinations of Bessel functions of several kinds as well as Bessel functions, themselves, have been investigated by many authors. Motivated the works of both Garg and Mittal and Ali, very recently, Choi and Agarwal gave two interesting unified integrals involving the Bessel function of the first kind $J_{\nu}(z)$. In the present sequel to the aforementioned investigations and some of the earlier works listed in the reference, we present two generalized integral formulas involving a product of Bessel functions of the first kind, which are expressed in terms of the generalized Lauricella series due to Srivastava and Daoust. Some interesting special cases and (potential) usefulness of our main results are also considered and remarked, respectively.

• Journal of the Korean Mathematical Society
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• v.33 no.1
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• pp.57-68
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• 1996

In the classical analysis there are various theorems which permit us to interchange limits and infinite sums, limits and integrals, integrals and infinite sums, etc. The infinite products as well as the infinite series play an important role in different branches of mathematics.

• Korean Journal of Mathematics
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• v.23 no.1
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• pp.47-64
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• 2015

We express generalized Fourier-Feynman transform and convolution product of functionals in a Banach algebra $\mathcal{S}(L^2_{a,b}[0,T])$ as limits of function space integrals on $C_{a,b}[0,T]$. Moreover we obtain change of scale formulas for function space integrals related with generalized Fourier-Feynman transform and convolution product of these functionals.

• Kyungpook Mathematical Journal
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• v.48 no.2
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• pp.165-171
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• 2008

The aim of this paper is to evaluate four finite integrals involving the product of Srivastava's polynomials, a generalized hypergeometric function and $\bar{H}$-function proposed by Inayat Hussian which contains a certain class of Feynman integrals. At the end, we give an application of our main findings by connecting them with the Riemann-Liouville type of fractional integral operator. The results obtained by us are basic in nature and are likely to find useful applications in several fields notably electric networks, probability theory and statistical mechanics.