To send content items to your account,
please confirm that you agree to abide by our usage policies.
If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account.
Find out more about sending content to .
To send content items to your Kindle, first ensure email@example.com
is added to your Approved Personal Document E-mail List under your Personal Document Settings
on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part
of your Kindle email address below.
Find out more about sending to your Kindle.
Note you can select to send to either the @free.kindle.com or @kindle.com variations.
‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi.
‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.
Our aim in this paper is to deal with integrability of maximal functions for Herz–Morrey spaces on the unit ball with variable exponent
and for double phase functionals
is nonnegative, bounded and Hölder continuous of order
. We also establish Sobolev type inequality for Riesz potentials on the unit ball.
Our aim in this paper is to deal with Sobolev's embeddings for Sobolev–Orlicz functions with ∇u ∈ Lp(·) logLq(·)(Ω) for Ω ⊂ n. Here p and q are variable exponents satisfying natural continuity conditions. Also the case when p attains the value 1 in some parts of the domain is included in the results.
In the previous paper , introducing the notions of potentials and of capacity associated with a convex function Φ given on a regular functional space we discussed potential theoretic properties of the gradient ∇Φ which were originally introduced and studied by Calvert  for a class of nonlinear monotone operators in Sobolev spaces. For example:
(i)The modulus contraction operates.
(ii)The principle of lower envelope holds.
(iii)The domination principle holds.
(iv)The contraction Tk onto the real interval [0, k] (k > 0) operates.
(v)The strong principle of lower envelope holds.
(vi)The complete maximum principle holds.
Email your librarian or administrator to recommend adding this to your organisation's collection.