Necessary and sufficient conditions for boundedness of the maximal operator in local Morrey-type spaces

By Victor Burenkov, H. Guliyev. 2004

160 citations recorded by the source corpus.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/55473f2c2a5ed9d7de843201e36ed952281a2f8c

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Citations in the corpus

Weighted Hardy and potential operators in the generalized Morrey spaces (2011, unknown): “Obviously, L (Ω) ⊂ L p,φ loc;x0 The spaces L p,φ(Ω), L p,φ loc;x0 (Ω) are known under the names of global and local Morrey spaces, see for instance [7,8].”
SUFFICIENT CONDITIONS FOR BOUNDEDNESS OF THE RIESZ POTENTIAL IN LOCAL MORREY-TYPE SPACES (2007, unknown): “The boundedness of various integral operators in the spaces GMp1,w was studied by T. Mizuhara [11] and E. Nakai [13]. In [ 6 , 7] the boundedness of”
Boundedness of Maximal and Singular Operators in Morrey Spaces with Variable Exponent (2008, background): “Mp q (see [25], [27], [15], [1] for the definition and some properties of Mp q). For the boundedness of maximal and singular integrals in the spaces Mp q we refer to [4], [11], [ 3 ], [30].”
Boundedness of the fractional maximal operator in local Morrey-type spaces (2010, background): “In [ 5 , 6] the boundedness of the maximal operator M from LMp1 1,w1 to LMp2 2,w2 and from GMp1 1,w1 to GMp2 2,w2 was investigated.”
Weighted multilinear Hardy operators and commutators (2014, background): “Here the space CṀO(R) was first introduced by Lu and Yang in [19], and the space Ḃ(R) is a generalization of CṀO(R) introduced by Alvarez, Guzman-Partida and Lakey in [1]; see also [2].”
Necessary and sufficient conditions for the boundedness of fractional maximal operators in local Morrey-type spaces (2007, methodology): “In [3,4] the following statement was proved.”
Maximal functions, potentials and singular integrals in grand Morrey spaces (2011, background): “Finally we mention that necessary and sufficient conditions for the boundedness of maximal operators and Riesz potentials in the local Morrey-type spaces were derived in [17,18].”
Weighted Hardy and singular operators in Morrey spaces (2008, background): “In the context of Morrey spaces, Hardy operators seem to have appeared only in [8] i a different aspect: the problem of the boundedness of the maximal operator in local M orrey spaces was reduced to an Lp-boundedness of Hardy operators on a cone of monotone functi ons.”
Maximal functions and potentials in variable exponent Morrey spaces with non-doubling measure (2010, background): “For weighted estimates of maximal functions and potentials in local Morrey spaces on R, see [7,8].”
Description of interpolation spaces for local Morrey-type spaces (2010, background): “The boundedness of the classical operators of function theory in the Morrey spaces and in general Morrey-type spaces was studied in [1, 8, 12, 14, 3–6].”
Boundedness of the maximal, potential and singular operators in the generalized variable exponent Morrey spaces (2010, background): “Generalized Morrey spaces of such a kind in the case of constant p were studied in [4], [13], [26], [28], [30], [31].”
Necessary and Sufficient Conditions for the Boundedness of the Riesz Potential in Local Morrey-type Spaces (2008, background): “Assume that |x |− r ≤ ρ ≤| x|. Then inequality (24) is established in the proof of Lemma 2i n [ 6 ].”
Morrey-Campanato Spaces: an Overview (2013, unknown): “Guliyev [18] (2004), such space L(R) is “reasonable” under the assumptions ∥∥∥∥ 1 φ1/p ∥∥∥∥ Lθ(t1,∞) < ∞ and ∥∥∥∥ r n p φ1/p ∥∥∥∥ L(0,t2) < ∞”