Dirichlet-Type Problems for Certain Beltrami Equations
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DOI: 10.1007/s00009-021-01760-2
Abstract: In this paper, we shall be interested in solving Dirichlet-type problems for solutions of certain classes of Beltrami equations, to be called $$\beta -$$ analytic. Orthogonal decomposition of the corresponding Sobolev space as well as… read more here.
Keywords: problems certain; dirichlet type; certain beltrami; type problems ... See more keywords
Generalized Cesàro Operators on Dirichlet-Type Spaces
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DOI: 10.1007/s10473-022-0111-2
Abstract: In this note, we introduce and study a new kind of generalized Cesaro operators $\mathcal{C}_{\mu}$, induced by a positive Borel measure $\mu$ on $[0, 1)$, between the Dirichlet-type spaces. We characterize the measures $\mu$ for… read more here.
Keywords: generalized ces; type spaces; operators dirichlet; dirichlet type ... See more keywords
Approximation of Invariant Subspaces in Some Dirichlet-Type Spaces
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DOI: 10.1007/s11785-017-0706-0
Abstract: The Hilbert space $$\mathcal {D}_{2}$$D2 is the space of all holomorphic functions f defined on the open unit disc $$\mathbb {D}$$D such that $${f}^{'}$$f′ is in the Hardy Hilbert space $$\mathbf {H}^2.$$H2. In this paper,… read more here.
Keywords: subspaces dirichlet; space; type spaces; approximation invariant ... See more keywords
Superposition operators, Hardy spaces, and Dirichlet type spaces
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DOI: 10.1016/j.jmaa.2018.03.044
Abstract: Abstract For 0 p ∞ and α > − 1 the space of Dirichlet type D α p consists of those functions f which are analytic in the unit disc D and satisfy ∫ D… read more here.
Keywords: space; dirichlet type; hardy spaces; operators hardy ... See more keywords
Möbius invariant Dirichlet type spaces
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DOI: 10.1016/j.jmaa.2018.06.059
Abstract: Abstract Let D μ , p be a Dirichlet type space induced by a positive parameter p and a positive Borel measure μ on the open unit disk. Denote by M ( D μ ,… read more here.
Keywords: space; type spaces; measure; bius invariant ... See more keywords
Positive solutions to singular Dirichlet-type boundary value problems of nonlinear fractional differential equations
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DOI: 10.1186/s13662-018-1627-6
Abstract: In this paper, by using the properties of the Green function, u0$u_{0}$-positive operator and Gelfand’s formula, some properties of the first eigenvalue corresponding to the relevant operator are obtained. Based on these properties, the fixed… read more here.
Keywords: positive solutions; singular dirichlet; type boundary; dirichlet type ... See more keywords
Embedding of Dirichlet type spaces $\mathcal {D}^{p}_{p-1 }$ into tent spaces and Volterra operators
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DOI: 10.4153/s0008439520000764
Abstract: Abstract In this paper, we study the boundedness and compactness of the inclusion mapping from Dirichlet type spaces $\mathcal {D}^{p}_{p-1 }$ to tent spaces. Meanwhile, the boundedness, compactness, and essential norm of Volterra integral operators… read more here.
Keywords: dirichlet type; type spaces; spaces mathcal; tent spaces ... See more keywords