Relation between Solvability and a Regularity of Convolution Operators in K′p, p&gt;1

Pahk, Dae Hyeon; Sohn, Byung Keun

doi:10.1006/jmaa.1994.1242

Journal of Mathematical Analysis and Applications

1994

DOI: 10.1006/jmaa.1994.1242

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Relation between Solvability and a Regularity of Convolution Operators in K′p, p>1

Dae Hyeon Pahk¹,

Byung Keun Sohn²

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“…In [6] ( [7], resp.) we also study the same problem in the space of distributions which grow no faster than exp(/c x p ) (exp(M(/cr)), resp.…”

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confidence: 99%

On the Solvability of Convolution Equations in Beurling's Distributions

Pahk¹,

Sohn²

1996

Publ. Res. Inst. Math. Sci.

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Let &' w be the space of Beurling's generalized distributions on E n and % w the spaces of generalized distributions which has compact support We show that, for S e % w , S * & w = & w is equivalent to the following: Every generalized distribution u e % w with S * u e S. Abdullah [1] proves that, for a generalized distribution S having compact support, the followings are equivalent; (a) There exists positive constants A, C such that sup S0r+?) > \x\< A>(io In this paper we show another property which is equivalent to the above. Before stating our main theorem we briefly introduce the space of generalized distributions of Beurling type and the related results which we need in this paper. For details we refer to [3] .We denote by M c the set of all real valued functions w on R n satisfying the following conditions; (a) 0 = w;(0) < wCf+fl) < tt>(?) + M>07), f, 7?eR" (7) w;(f) > a + b log(l+ | f |) for some constants a and b > 0.

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“…In [6] ( [7], resp.) we also study the same problem in the space of distributions which grow no faster than exp(/c x p ) (exp(M(/cr)), resp.…”

mentioning

confidence: 99%

On the Solvability of Convolution Equations in Beurling's Distributions

Pahk¹,

Sohn²

1996

Publ. Res. Inst. Math. Sci.

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On Solvability of Convolution Equations in Spaces of Generalized Distributions with Restricted Growth

Abdullah

1999

Journal of Mathematical Analysis and Applications

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On Hankel Convolution Equations in Distribution Spaces

Rodríguez-Mesa¹

1999

Rocky Mountain J. Math.

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Relation between Solvability and a Regularity of Convolution Operators in K′p, p>1

Cited by 3 publications

References 0 publications

On the Solvability of Convolution Equations in Beurling's Distributions

On the Solvability of Convolution Equations in Beurling's Distributions

On Solvability of Convolution Equations in Spaces of Generalized Distributions with Restricted Growth

On Hankel Convolution Equations in Distribution Spaces

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