Displaying similar documents to “The ℒ ν ( ρ ) -transformation on McBride’s spaces of generalized functions”

On conditions for the boundedness of the Weyl fractional integral on weighted L p spaces

Liliana De Rosa, Alberto de la Torre (2004)

Commentationes Mathematicae Universitatis Carolinae

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In this paper we give a sufficient condition on the pair of weights ( w , v ) for the boundedness of the Weyl fractional integral I α + from L p ( v ) into L p ( w ) . Under some restrictions on w and v , this condition is also necessary. Besides, it allows us to show that for any p : 1 ≤ p < ∞ there exist non-trivial weights w such that I α + is bounded from L p ( w ) into itself, even in the case α > 1 .

Weak solutions for elliptic systems with variable growth in Clifford analysis

Yongqiang Fu, Binlin Zhang (2013)

Czechoslovak Mathematical Journal

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In this paper we consider the following Dirichlet problem for elliptic systems: D A ( x , u ( x ) , D u ( x ) ) ¯ = B ( x , u ( x ) , D u ( x ) ) , x ∈ Ω , u ( x ) = 0 , x ∈ ∂ Ω , where D is a Dirac operator in Euclidean space, u ( x ) is defined in a bounded Lipschitz domain Ω in ℝ n and takes value in Clifford algebras. We first introduce variable exponent Sobolev spaces of Clifford-valued functions, then discuss the properties of these spaces and the related operator theory in these spaces. Using the Galerkin method, we obtain the existence of weak solutions to the scalar part of the...